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At least 631 records · Page 35

Ubiquitous Wireless Smart Sensing and Control

Need new technologies to reliably and safely have humans interact within sensored environments (integrated user interfaces, physical and cognitive augmentation, training, and human-systems integration tools). Areas of focus include: radio frequency identification (RFID), motion tracking, wireless communication, wearable computing, adaptive training and decision support systems, and tele-operations. The challenge is developing effective, low cost/mass/volume/power integrated monitoring systems to assess and control system, environmental, and operator health; and accurately determining and controlling the physical, chemical, and biological environments of the areas and associated environmental control systems.

Wagner, Raymond↗

Small Stirling Technology Exploration Power for Future Space Science Missions

High efficiency dynamic Radioisotope Power Systems (RPS) could be mission enabling for low power space applications such as small probes, landers rovers, and communication repeaters. These applications would contain science instruments and be distributed across planetary surfaces or near objects of interest where solar flux is insufficient for using solar cells. Small RPS could be used to provide power for sensing radiation, temperature, pressure, seismic activity, and other measurements of interest to planetary scientists. Small RPS would use fractional versions of the General Purpose Heat Source (GPHS) or Light Weight Radioisotope Heater Units (LWRHU), to heat power conversion technologies. Dynamic power systems are capable of three to four times higher conversion efficiency compared to static power conversion technologies, and would provide an equal amount of power using less fuel or more power using an equal amount of fuel. Providing spacecraft with more power could decrease duty cycling of basic functions and, therefore, increase the quality and abundance of science data. NASA GRC is developing a low power dynamic RPS that would convert heat from multiple LWRHU to one watt of usable direct current electric power for spacecraft instrumentation and communication. The power system could be used to charge batteries or capacitors for higher power burst usage. The initial design, called Small Stirling Technology Exploration Power (smallSTEP), is around 3 kg, 11 cm diameter X 32 cm long, and converts 8 watts of heat to one watt of electricity using a Stirling convertor. This low power conversion system represents a new class of RPS with power levels two orders of magnitude lower than prototypes currently being developed for space applications under NASA contracts. Development of the 1-watt RPS includes maturation of convertor and controller designs, performance evaluation of an evacuated metal foil insulation, and development of system interfaces. Initial demonstration of the subsystems has been completed in a laboratory environment and a higher fidelity system is being pursued for demonstration in relevant environments for use on small spacecraft needed to carry out future space science missions.

Wilson, Scott D.↗

Probability Index of Low Stratus and Fog at Dawn using Dual Geostationary Satellite Observations from COMS and FY-2D near the Korean Peninsula

We developed a new remote sensing method for detecting low stratus and fog (LSF) at dawn in terms of probability index (PI) of LSF from simultaneous stereo observations of two geostationary-orbit satellites; the Korean Communication, Ocean, and Meteorological Satellite (COMS; 128.2°E); and the Chinese FengYun satellite (FY-2D; 86.5°E). The algorithm was validated near the Korean Peninsula between the months of April and August from April 2012 to June 2015, by using surface observations at 45 meteorological stations in South Korea. The optical features of LSF were estimated by using satellite retrievals and simulated data from the radiative transfer model. The PI was calculated using the combination of three satellite-observed variables: 1) the reflectance at 0.67 μm (R(0.67)) from COMS, and 2) the FY-2D R(0.67) minus the COMS R(0.67) (△R(0.67)) and (3) the FY-2D-COMS difference in the brightness temperature difference between 3.7 and 11.0 μm (ΔBTD(3.7-11)). The three variables, adopted from the top three probability of detection (POD) scores for their fog detection thresholds: △R(0.67) (0.82) > ΔBTD(3.7-11) (0.73) > R(0.67) (0.70) > BTD(3.7-11) (0.51). The LSF PI for this algorithm was significantly better in the two case studies compared to that using COMS only (i.e., R(0.67) or BTD(3.7-11)), so that this improvement was due to △R(0.67) and ΔBTD(3.7-11). Overall, PI in the LSF spatial distribution has the merits of a high detection rate, a specific probability display, and a low rate of seasonality and variability in detection accuracy. Therefore, PI would be useful for monitoring LSF in near-real-time, and to further its forecast ability, using next-generation satellites.

fog↗

Small Stirling Technology Exploration Power for Future Space Science Missions

High efficiency dynamic Radioisotope Power Systems (RPS) could be mission enabling for low power space applications such as small probes, landers rovers, and communication repeaters. These applications would contain science instruments and be distributed across planetary surfaces or near objects of interest where solar flux is insufficient for using solar cells. Small RPS could be used to provide power for sensing radiation, temperature, pressure, seismic activity, and other measurements of interest to planetary scientists. Small RPS would use fractional versions of the General Purpose Heat Source (GPHS) or Light Weight Radioisotope Heater Units (LWRHU), to heat power conversion technologies. Dynamic power systems are capable of three to four times higher conversion efficiency compared to static power conversion technologies, and would provide an equal amount of power using less fuel or more power using an equal amount of fuel. Providing spacecraft with more power could decrease duty cycling of basic functions and, therefore, increase the quality and abundance of science data. NASA Glenn Research Center (GRC) is developing a low power dynamic RPS that would convert heat from multiple LWRHU to one watt of usable direct current electric power for spacecraft instrumentation and communication. The power system could be used to charge batteries or capacitors for higher power burst usage. The initial design, called Small Stirling Technology Exploration Power (smallSTEP), is around 3 kg, 11 cm diameter X 32 cm long, and converts 8 watts of heat to one watt of electricity using a Stirling convertor. This low power conversion system represents a new class of RPS with power levels two orders of magnitude lower than prototypes currently being developed for space applications under NASA contracts. Development of the 1-watt RPS includes maturation of convertor and controller designs, performance evaluation of an evacuated metal foil insulation, and development of system interfaces. Initial demonstration of the subsystems has been completed in a laboratory environment and a higher fidelity system is being pursued for demonstration in relevant environments for use on small spacecraft needed to carry out future space science missions.

Wilson, Scott↗

Enabling Secure and Resilient XFC: A Software/Hardware-Security Co-Design Approach

Extremely fast charging (XFC) has the potential to reduce the charging time of battery electric vehicles (BEV) to be equivalent to the filling time of internal combustion engine vehicles (ICEV), thus eliminating one of the few advantages ICEV still poses for light- and heavy-duty vehicles. Enabling XFC will, however, require coordination and cooperation between the grid, charging stations, and the vehicles themselves, which leads to an inevitable increase in the attack surface for all systems combined. In securing the overall system, we must not only embrace traditional cybersecurity, which is chiefly concerned with communications and the operation of digital systems, but also cyber-physical systems security as the proper operation of XFC is critically dependent on systems’ abilities to know about (sense) and interact with (actuate) the physical world. The project team consists of academic and industry researchers with backgrounds in cybersecurity, cyber-physical systems security, learning in adversarial environments, transportation security, grid security and resilience, wireless power transfer, converter design, and battery management systems.

33 ADVANCED PROPULSION SYSTEMS↗

Space flight and the skeleton: lessons for the earthbound

Loss of bone during extended space flight has long been a concern that could limit the ability of humans to explore the universe. Surprisingly, the available data do not support the concept that weightlessness leads inexorably to a depleted skeleton unable to withstand the stress of a return to a 1-g environment. Nevertheless, some bone loss does occur, especially in those bones most stressed by gravity prior to flight, which provides confirmation of the proposal formulated over a century ago by Julius Wolff that mechanical stress determines the form and function of bone. Although the phenomenon of bone loss with skeletal unloading, whether by space flight or immobilization or just taking a load off your feet (literally) is well established, the mechanisms by which bone senses load and adjusts to it are not so clear. What actually is the stimulus, and what are the sensors? What are the target cells? How do the sensors communicate the message into the cells, and by what pathways do the cells respond? What is the role of endocrine, factors vs. paracrine or autocrine factors in mediating or modulating the response? None of these questions has been answered with certainty, but, as will become apparent in this review, we have some clues directing us to the answers. Although the focus of this review concerns space flight, it seems highly likely that the mechanisms mediating the transmission of mechanical load to changes in bone formation and resorption apply equally well to all forms of disuse osteoporosis and are likely to be the same mechanisms affected by other etiologies of osteoporosis.

unmanned↗

Spaceflight and the skeleton: lessons for the earthbound

Loss of bone during extended space flight has long been a concern that could limit the ability of humans to explore the universe. Surprisingly the available data do not support the concept that weightlessness leads inexorably to a depleted skeleton unable to withstand the stress of a return to a 1g environment. Nevertheless, some bone loss does occur especially in those bones most stressed by gravity prior to flight, providing confirmation of the proposal formulated over a century ago by Julius Wolff that mechanical stress determines the form and function of bone. Although the phenomenon of bone loss with skeletal unloading, whether by space flight or immobilization or just taking a load off your feet (literally) is well established, the mechanisms by which bone senses load and adjusts to it are not so clear. What actually is the stimulus and what are the sensors? What are the target cells? How do the sensors communicate the message into the cells, and by what pathways do the cells respond? What is the role of endocrine factors versus paracrine or autocrine factors in mediating or modulating the response? None of these questions has been answered with certainty, but as will become apparent in this review, we have some clues directing us to the answers. Although the focus of this review concerns space flight, it seems highly likely that the mechanisms mediating the transmission of mechanical load to changes in bone formation and resorption apply equally well to all forms of disuse osteoporosis, and are likely to be the same mechanisms affected by other etiologies of osteoporosis.

NASA Discipline Musculoskeletal↗

A Distributed Data Architecture for 2001 Mars Odyssey Data Distribution

Newer instruments and communications techniques have given scientists unprecedented amounts of data, more than can be feasibly distributed through traditional methods such as mailed CD-ROM's. Leveraging the web makes sense since it enables scientists to request specific data and retrieve products as soon as they're available. Yet defining the middleware system to support such an application has remained just out of reach, until Odyssey. For the first time ever, data from all Odyssey mission instruments were made available through a single system immediately upon delivery to the Planetary Data System (PDS). The Object Oriented Data Technology (OODT) software made such an application possible.

distributed↗

Mars Reconnaissance Orbiter Navigation Strategy for Mars Science Laboratory Entry, Descent and Landing Telecommunication Relay Support

The Mars Reconnaissance Orbiter (MRO) is an orbiting asset that performs remote sensing observations in order to characterize the surface, subsurface and atmosphere of Mars. To support upcoming NASA Mars Exploration Program Office objectives, MRO will be used as a relay communication link for the Mars Science Laboratory (MSL) mission during the MSL Entry, Descent and Landing sequence. To do so, MRO Navigation must synchronize the MRO Primary Science Orbit (PSO) with a set of target conditions requested by the MSL Navigation Team; this may be accomplished via propulsive maneuvers. This paper describes the MRO Navigation strategy for and operational performance of MSL EDL relay telecommunication support.

Mars Reconnaissance Orbiter (MRO)↗

Airborne Radar for sUAS Sense and Avoid

A primary challenge for the safe integration of small UAS operations into the National Airspace System (NAS) is traffic deconfliction, both from manned and unmanned aircraft. The UAS Traffic Management (UTM) project being conducted at the National Aeronautics and Space Administration (NASA) considers a layered approach to separation provision, ranging from segregation of operations through airspace volumes (geofences) to autonomous sense and avoid (SAA) technologies for higher risk, densely occupied airspace. Cooperative SAA systems, such as Automatic Dependent Surveillance-Broadcast (ADS-B) and/or vehicle-to-vehicle communication systems provide significant additional risk mitigation but they fail to adequately mitigate collision risks for non-cooperative (non-transponder equipped) airborne aircraft. The RAAVIN (Radar on Autonomous Aircraft to Verify ICAROUS Navigation) flight test being conducted by NASA and the Mid-Atlantic Aviation Partnership (MAAP) was designed to investigate the applicability and performance of a prototype, commercially available sUAS radar to detect and track non-cooperative airborne traffic, both manned and unmanned. The radar selected for this research was a Frequency Modulated Continuous Wave (FMCW) radar with 120 degree azimuth and 80 degree elevation field of view operating at 24.55GHz center frequency with a 200 MHz bandwidth. The radar transmits 2 watts of power thru a Metamaterial Electronically Scanning Array antenna in horizontal polarization. When the radar is transmitting, personnel must be at least 1 meter away from the active array to limit nonionizing radiation exposure. The radar physical dimensions are 18.7cm by 12.1cm by 4.1cm and it weighs less than 820 grams making it well suited for installation on small UASs. The onboard, SAA capability, known as ICAROUS, (Independent Configurable Architecture for Reliable Operations of Unmanned Systems), developed by NASA to support sUAS operations, will provide autonomous guidance using the traffic radar tracks from the onboard radar. The RAAVIN set of studies will be conducted in three phases. The first phase included outdoor, ground-based radar evaluations performed at the Virginia Tech’s Kentland Farm testing range in Blacksburg, VA. The test was designed to measure how well the radar could detect and track a small UAS flying in the radar’s field of view. The radar was used to monitor 5 test flights consisting of outbound, inbound and crossing routes at different ranges and altitudes. The UAS flown during the ground test was the Inspire 2, a quad copter weighing less than 4250 grams (10 pounds) at maximum payload. The radar was set up to scan and track targets over its full azimuthal field of view from 0 to 40 degrees in elevation. The radar was configured to eliminate tracks generated from any targets located beyond 2000 meters from the radar and moving at velocities under 1.45 meters per second. For subsequent phases of the study the radar will be integrated with a sUAS platform to evaluate its performance in flight for SAA applications ranging from sUAS to manned GA aircraft detections and tracking. Preliminary data analysis from the first outdoor ground tests showed the radar performed well at tracking the vehicle as it flew outbound and repeatedly maintained a track out to 1000 meters (maximum 1387 meters) until the vehicle slowed to a stop to reverse direction to fly inbound. As the Inspire flew inbound tracks from beyond 800 meters, a reacquisition time delay was consistently observed between when the Inspire exceeds a speed of 1.45 meters per second and when the radar indicated an inbound target was present and maintained its track. The time delay varied between 6 seconds to over 37 seconds for the inbound flights examined, and typically resulted in about a 200 meter closure distance before the Inspire track was maintained. The radar performed well at both acquiring and tracking the vehicle as it flew crossing routes out past 400 meters across the azimuthal field of view. The radar and ICAROUS software will be integrated and flown on a BFD-1400-SE8-E UAS during the next phase of the RAAVIN project. The main goal at the conclusion of this effort is to determine if this radar technology can reliably support minimum requirements for SAA applications of sUAS. In particular, the study will measure the range of vehicle detections, lateral and vertical angular errors, false and missed/late detections, and estimated distance at closest point of approach after an avoidance maneuver is executed. This last metric is directly impacted by sensor performance and indicates its suitability for the task.

Szatkowski, George N.↗

Incorporation of Human Risk Directed Acyclic Graphs (DAG) With Mishap Investigations to Un-Silo Knowledge

NASA’s Human System Risk Board (HSRB) has been a central driver in efforts to understand, mitigate, and communicate the 29 human systems risks monitored by the board. As a result of the collaboration between research, operations, and technical authorities, large bodies of knowledge have been collected and digested to represent the current understanding of the risks. As a part of these bodies of knowledge, directed acyclic graphs (DAGs) have been developed to communicate the current understanding of the causal relationship of the hazards, contributing factors, countermeasures, other risks, and outcomes that contribute to the overall risk. This risk knowledge is applied in a theoretical sense for potential incidents during exploration even while informed by surveillance data. However, there have been mishaps and close calls during past space exploration that intersect with one or more of the Human System Risks DAGs and knowledge bases. The purpose of this exercise was to un-silo this risk knowledge and connect it to the close call of EVA 23 through the development of a DAG representing the intersection of the HSRB Risks and the events of the close call. The development of the DAG occurred through an iterative process, with each iteration expanding and/or refining the nodes and connections described by the source materials. In addition to the risk documentation developed by the HSRB, lessons learned and other mishap investigation documents were utilized to understand the events that led to water entering the helmet of a crewmember on the EVA. New nodes specific to the events of EVA 23 were interconnected with existing HSRB DAG nodes and edges. Nodes within the DAG were defined within a “DAG-tionary” with any updates to a definition that may have previously existed from the HSRB DAGs, and edges were recorded in a matrix. Both the DAG-tionary and matrix describe where nodes and edges are present across the Risk and Mishap DAG. This DAG will then be reviewed by experts outside of HSRB and HRP to confirm that interpretations of the non-health related events (such as the engineering nodes) are represented accurately. DISCUSSION This process highlighted a method by which the knowledge generated among the contributing members of the HSRB Risks can be effectively adapted and utilized through the tools employed by the Risk Custodian teams. By leveraging these tools, new context and insights to the information at hand can be brought forward to address current spaceflight challenges. Moreover, un-siloing this knowledge through future DAGs and other efforts can drive interprofessional collaboration and foster communication. This will enable teams to work together more effectively, leveraging their diverse expertise to tackle the complex challenges of space exploration and human research. Ultimately, this collaboration will bring NASA closer to achieve agency goals and contribute to the overall shared mission and vision.

Samuel Jacobs↗

A Simple and Accurate Energy-Detector-Based Transient Waveform Detection for Smart Grids: Real-World Field Data Performance

Integration of distributed energy sources, advanced meshed operation, sensors, automation, and communication networks all contribute to autonomous operations and decision-making processes utilized in the grid. Therefore, smart grid systems require sophisticated supporting structures. Furthermore, rapid detection and identification of disturbances and transients are a necessary first step towards situationally aware smart grid systems. This way, high-level monitoring is achieved and the entire system kept operational. Even though smart grid systems are unavoidably sophisticated, low-complexity algorithms need to be developed for real-time sensing on the edge and online applications to alert stakeholders in the event of an anomaly. In this study, the simplest form of anomaly detection mechanism in the absence of any a priori knowledge, namely, the energy detector (also known as radiometer in the field of wireless communications and signal processing), is investigated as a triggering mechanism, which may include automated alerts and notifications for grid anomalies. In contrast to the mainstream literature, it does not rely on transform domain tools; therefore, utmost design and implementation simplicity are attained. Performance results of the proposed energy detector algorithm are validated by real power system data obtained from the DOE/EPRI National Database of power system events and the Grid Signature Library.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Cramer-Rao Lower Bound for SoOp-R-Based Root-Zone Soil Moisture Remote Sensing

Signals of opportunity (SoOp) reflectometry (SoOp-R) is a maturing field for geophysical remote sensing as evidenced by the growing number of airborne and spaceborne experiments. As this approach receives more attention, it is worth analyzing SoOp-R’s capabilities to retrieve subsurface soil moisture (SM) by leveraging communication and navigation satellite transmitters. In this research, the CRLB is used to identify the effects of variable SoOp-R parameters on the best achievable estimation error for root-zone soil moisture (RZSM). This study investigates the use of multiple frequency, polarization, and incidence angle measurement configurations on a two-layered dielectric profile. The results also detail the effects of variable SM conditions on the capability of SoOp-R systems to predict subsurface SM. The most prevalent observation is the importance of using at least two frequencies to limit uncertainties from subsurface SM estimates. If at least two frequencies are used, the CRLB of a profile is retrievable within the root-zone depending on the surface SM content as well as the number of independent measurements of the profile. For a depth of 30 cm, it is observed that a CRLB corresponding to 4% RZSM estimation accuracy is achievable with as few as 2 dual-frequency-based SoOp-R measurements. For this depth, increasing number of measurements provided by polarization and incidence angle allow for sensing of increasingly wet SM profile structures. This study, overall, details a methodology by which SoOp-R receiver system can be designed to achieve a desired CRLB using a trade-off study between the available measurements and SM profile.

Signals of Opportunity (SoOp)↗

Liquid-Sensing Probe and Methods for Using the Same

A sensor assembly includes a main body, a sensor, and a filler. The main body includes an outer surface having a continuously-variable radius of curvature in at least one portion. A sensor in thermal communication with a region of that surface having relatively low radius of curvature is disposed in the assembly recessed from the outer surface. Liquid droplets adhered to the outer surface in this region tend to migrate to a distant location having a higher radius of curvature. The main body has low thermal conductivity. The filler has a relatively higher thermal conductivity and, in embodiments, fills an opening in the outer surface of the main body, providing a thermally-conductive pathway between the sensor and the surrounding environment via the opening. A probe having a plurality of such sensors, and methods of detecting the presence of liquid and phase transitions in a predetermined space are also disclosed.

Haberbusch, Mark S.↗

Optical sensing of magnetic fields using magnetically sensitive materials

The invention provides a method for measuring the magnetic field of an electromagnetic component having the steps of: instrumenting one or more portions of an electromagnetic component by placing an optical fiber in electromagnetic communication with the one or more portions of said electromagnetic component; energizing the electromagnetic component; interrogating the optical fiber using light and an optical detector; and determining changes in the magnetic field incident on the optical fiber based on the detected changes in the light received by the optical detector.

Ohodnicki, Paul↗

Horizon: A Proposal for Large Aperture, Active Optics in Geosynchronous Orbit

In 1999, NASA's New Millennium Program called for proposals to validate new technology in high-earth orbit for the Earth Observing-3 (NMP EO3) mission to fly in 2003. In response, we proposed to test a large aperture, active optics telescope in geosynchronous orbit. This would flight-qualify new technologies for both Earth and Space science: 1) a future instrument with LANDSAT image resolution and radiometric quality watching continuously from geosynchronous station, and 2) the Next Generation Space Telescope (NGST) for deep space imaging. Six enabling technologies were to be flight-qualified: 1) a 3-meter, lightweight segmented primary mirror, 2) mirror actuators and mechanisms, 3) a deformable mirror, 4) coarse phasing techniques, 5) phase retrieval for wavefront control during stellar viewing, and 6) phase diversity for wavefront control during Earth viewing. Three enhancing technologies were to be flight- validated: 1) mirror deployment and latching mechanisms, 2) an advanced microcontroller, and 3) GPS at GEO. In particular, two wavefront sensing algorithms, phase retrieval by JPL and phase diversity by ERIM International, were to sense optical system alignment and focus errors, and to correct them using high-precision mirror mechanisms. Active corrections based on Earth scenes are challenging because phase diversity images must be collected from extended, dynamically changing scenes. In addition, an Earth-facing telescope in GEO orbit is subject to a powerful diurnal thermal and radiometric cycle not experienced by deep-space astronomy. The Horizon proposal was a bare-bones design for a lightweight large-aperture, active optical system that is a practical blend of science requirements, emerging technologies, budget constraints, launch vehicle considerations, orbital mechanics, optical hardware, phase-determination algorithms, communication strategy, computational burdens, and first-rate cooperation among earth and space scientists, engineers and managers. This manuscript presents excerpts from the Horizon proposal's sections that describe the Earth science requirements, the structural -thermal-optical design, the wavefront sensing and control, and the on-orbit validation.

Chesters, Dennis↗

Clear Lake Volcanic Field Disasters: Creating a Deformation Record Using InSAR to Assess Hazards and Detect Volcanic Unrest in Clear Lake Volcanic Field

Clear Lake Volcanic Field (CLVF) in northern California is at a high threat potential for volcanic hazards. Eruptions leading to increased seismic activity could result in silicic domes, cinder cones, and flows that would be dangerous to the residential areas near the volcanic field. Remotely sensed Earth observations can reveal volcanic processes in the subsurface, which are essential to the timely monitoring of potential volcanic activity. In particular, Sentinel-1 C-band Synthetic Aperture Radar (C-SAR) and Digital Elevation Model (DEM) data capture relative surface deformation at unprecedented high spatial and temporal resolutions. Leveraging C-SAR and DEMs, we conducted interferometric analysis from January 2016 to December 2023. Our results demonstrate 1) the mean surface displacement velocity of the Clear Lake Volcanic Field is measured to undergo 5 to 10-centimeter scale deformation and shows a strong relationship with the surrounding faults, 2) apparent seasonal differences in rates of surface change, and 3) seismic activity associated with the geyser geothermal field has a strong association with cumulative surface displacement, with active fault zones having 2 to 5 cm of additional displacement. Results indicate that deformation is linked to deep pressure sources causing stresses on the surficial environment that should be considered in hazard mitigation. This study provides a baseline of historic deformation, aiding hazard analysts in communication efforts and streamlining decision-making for potential risks to region residents.

remote sensing↗

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

convergence↗