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Results for “Disciplined convex programming”

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All sources NASA NTRS DOE OSTI

DOE OSTI2017

Polyhedral approximation in mixed-integer convex optimization

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. Here, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming (DCP), and for generality and ease of implementation we use conic representations of the convex constraints. Although our framework requires a manual translation of existing models into DCP form, after performing this transformation on the MINLPLIB2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state-of-the-art solvers like Bonmin, SCIP, and Artelys Knitro.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2012

Active Mirror Predictive and Requirements Verification Software (AMP-ReVS)

This software is designed to predict large active mirror performance at various stages in the fabrication lifecycle of the mirror. It was developed for 1-meter class powered mirrors for astronomical purposes, but is extensible to other geometries. The package accepts finite element model (FEM) inputs and laboratory measured data for large optical-quality mirrors with active figure control. It computes phenomenological contributions to the surface figure error using several built-in optimization techniques. These phenomena include stresses induced in the mirror by the manufacturing process and the support structure, the test procedure, high spatial frequency errors introduced by the polishing process, and other process-dependent deleterious effects due to light-weighting of the mirror. Then, depending on the maturity of the mirror, it either predicts the best surface figure error that the mirror will attain, or it verifies that the requirements for the error sources have been met once the best surface figure error has been measured. The unique feature of this software is that it ties together physical phenomenology with wavefront sensing and control techniques and various optimization methods including convex optimization, Kalman filtering, and quadratic programming to both generate predictive models and to do requirements verification. This software combines three distinct disciplines: wavefront control, predictive models based on FEM, and requirements verification using measured data in a robust, reusable code that is applicable to any large optics for ground and space telescopes. The software also includes state-of-the-art wavefront control algorithms that allow closed-loop performance to be computed. It allows for quantitative trade studies to be performed for optical systems engineering, including computing the best surface figure error under various testing and operating conditions. After the mirror manufacturing process and testing have been completed, the software package can be used to verify that the underlying requirements have been met.

Basinger, Scott A.↗

DOE OSTI2021

Collaborative Decision Approach for Electricity Pricing-demand Response Stackelberg Game

Demand response programs are considered as a valuable resource in smart grids that provide several advantages of load shifting, peak load reduction, mediating intermittency of renewable energy integration, etc. Flexible price-based incentives have been recognized as a critical strategy in motivating and compensating consumers' load adjustment actions for successful implementation of demand response. Game theoretical approaches, especially Stackelberg games are popularly adopted to model the relationship between electricity price and customers' demand response and solved by the classical centralized backward induction (BI) method. However, the BI method generally requires convexity of the follower's model for necessary optimality conditions, and the computational time of any centralized approach increases sharply with larger problem instances. In this paper, the Stackelberg game of electricity pricing-demand response between a distribution system operator (DSO) and load aggregators (LAs) is decomposed based on a collaborative optimization (CO) framework, where each LA is treated as a discipline with its own domain constraints (e.g. building temperature control), while the DSO at the system level tries to reduce the solution discrepancy and guide the searching towards optimality. Several groups of comparison experiments have demonstrated the effectiveness of the proposed collaborative decision approach in solving the demand response game.

Chen, Yang↗

NASA NTRS1989

The pattern of secondary root formation in curving roots of Arabidopsis thaliana (L.) Heynh

A gravitational stimulus was used to induce the curvature of the main root of Arabidopsis thaliana. The number of secondary roots increased on the convex side and decreased on the concave side of any curved main root axes in comparison with straight roots used as the control. The same phenomenon was observed with the curved main roots of plants grown on a clinostat and of mutant plants exhibiting random root orientation. The data suggest that the pattern of lateral root formation is associated with curvature but is independent of the environmental stimuli used to induce curvature.

Non-NASA Center↗

NASA NTRS2003

Touch and gravitropic set-point angle interact to modulate gravitropic growth in roots

Plant roots must sense and respond to a variety of environmental stimuli as they grow through the soil. Touch and gravity represent two of the mechanical signals that roots must integrate to elicit the appropriate root growth patterns and root system architecture. Obstacles such as rocks will impede the general downwardly directed gravitropic growth of the root system and so these soil features must be sensed and this information processed for an appropriate alteration in gravitropic growth to allow the root to avoid the obstruction. We show that primary and lateral roots of Arabidopsis do appear to sense and respond to mechanical barriers placed in their path of growth in a qualitatively similar fashion. Both types of roots exhibited a differential growth response upon contacting the obstacle that directed the main axis of elongation parallel to the barrier. This growth habit was maintained until the obstacle was circumvented, at which point normal gravitropic growth was resumed. Thus, the gravitational set-point angle of the primary and lateral roots prior to encountering the barrier were 95 degrees and 136 degrees respectively and after growing off the end of the obstacle identical set-point angles were reinstated. However, whilst tracking across the barrier, quantitative differences in response were observed between these two classes of roots. The root tip of the primary root maintained an angle of 136 degrees to the horizontal as it traversed the barrier whereas the lateral roots adopted an angle of 154 degrees. Thus, this root tip angle appeared dependent on the gravitropic set-point angle of the root type with the difference in tracking angle quantitatively reflecting differences in initial set-point angle. Concave and convex barriers were also used to analyze the response of the root to tracking along a continuously varying surface. The roots maintained the a fairly fixed angle to gravity on the curved surface implying a constant resetting of this tip angle/tracking response as the curve of the surface changed. We propose that the interaction of touch and gravity sensing/response systems combine to strictly control the tropic growth of the root. Such signal integration is likely a critical part of growth control in the stimulus-rich environment of the soil. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Discipline Plant Biology↗

NASA NTRS1991

Computer-based video digitizer analysis of surface extension in maize roots: kinetics of growth rate changes during gravitropism

We used a video digitizer system to measure surface extension and curvature in gravistimulated primary roots of maize (Zea mays L.). Downward curvature began about 25 +/- 7 min after gravistimulation and resulted from a combination of enhanced growth along the upper surface and reduced growth along the lower surface relative to growth in vertically oriented controls. The roots curved at a rate of 1.4 +/- 0.5 degrees min-1 but the pattern of curvature varied somewhat. In about 35% of the samples the roots curved steadily downward and the rate of curvature slowed as the root neared 90 degrees. A final angle of about 90 degrees was reached 110 +/- 35 min after the start of gravistimulation. In about 65% of the samples there was a period of backward curvature (partial reversal of curvature) during the response. In some cases (about 15% of those showing a period of reverse bending) this period of backward curvature occurred before the root reached 90 degrees. Following transient backward curvature, downward curvature resumed and the root approached a final angle of about 90 degrees. In about 65% of the roots showing a period of reverse curvature, the roots curved steadily past the vertical, reaching maximum curvature about 205 +/- 65 min after gravistimulation. The direction of curvature then reversed back toward the vertical. After one or two oscillations about the vertical the roots obtained a vertical orientation and the distribution of growth within the root tip became the same as that prior to gravistimulation. The period of transient backward curvature coincided with and was evidently caused by enhancement of growth along the concave and inhibition of growth along the convex side of the curve, a pattern opposite to that prevailing in the earlier stages of downward curvature. There were periods during the gravitropic response when the normally unimodal growth-rate distribution within the elongation zone became bimodal with two peaks of rapid elongation separated by a region of reduced elongation rate. This occurred at different times on the convex and concave sides of the graviresponding root. During the period of steady downward curvature the elongation zone along the convex side extended farther toward the tip than in the vertical control. During the period of reduced rate of curvature, the zone of elongation extended farther toward the tip along the concave side of the root. The data show that the gravitropic response pattern varies with time and involves changes in localized elongation rates as well as changes in the length and position of the elongation zone. Models of root gravitropic curvature based on simple unimodal inhibition of growth along the lower side cannot account for these complex growth patterns.

NASA Discipline Plant Biology↗

NASA NTRS1992

Physiological asymmetry in etiolated pea epicotyls: relation to patterns of auxin distribution and phototropic behavior

Etiolated pea seedlings require transformation of Pr phytochrome to Pfr before they display optimal phototropic response to unilateral blue light. This study investigates the possible role of auxin transport in explaining these phenomena. Labeled [2-14C]IAA applied to the intact terminal buds of dark-grown and red light-treated pea seedlings was measured 210 min later on the shaded and illuminated sides of the epicotyl as a function of direction and duration of irradiation with blue light. Totally darkened epicotyls show an asymmetry in distribution of radioactivity in the upper growth zone of the epicotyl, in favor of the side under the concave part of the apical hook. Red light, which greatly potentiates curvature toward subsequent unilateral blue light, lowers this asymmetry. Blue light directed to the epicotyl of red-pretreated plants in a plane parallel to the hook and from the side bearing the convex portion of the hook induces positive phototropic curvature as well as a surplus of radioactivity on the illuminated side of the upper epicotyl and on the shaded side of the lower growth zone of the epicotyl. Light directed to the side bearing the concave part of the hook also causes an accumulation of counts in the upper part of the lighted side but produces neither curvature of the epicotyl nor accumulation of counts in the lower shaded side. Because of this built-in physiological asymmetry in the growth zone just below the apical hook, it is difficult to explain the effects of red and blue light on curvature in terms of patterns of auxin distribution alone.

NASA Program Space Biology↗

NASA NTRS1992

Stimulation of root elongation and curvature by calcium

Ca2+ has been proposed to mediate inhibition of root elongation. However, exogenous Ca2+ at 10 or 20 millimolar, applied directly to the root cap, significantly stimulated root elongation in pea (Pisum sativum L.) and corn (Zea mays L.) seedlings. Furthermore, Ca2+ at 1 to 20 millimolar, applied unilaterally to the caps of Alaska pea roots, caused root curvature away from the Ca2+ source, which was caused by an acceleration of elongation growth on the convex side (Ca2+ side) of the roots. Roots of an agravitropic pea mutant, ageotropum, responded to a greater extent. Roots of Merit and Silver Queen corn also responded to Ca2+ in similar ways but required a higher Ca2+ concentration than that of pea roots. Roots of all other cultivars tested (additional four cultivars of pea and one of corn) curved away from the unilateral Ca2+ source as well. The Ca(2+)-stimulated curvature was substantially enhanced by light. A Ca2+ ionophore, A23187, at 20 micromolar or abscisic acid at 0.1 to 100 micromolar partially substituted for the light effect and enhanced the Ca(2+)-stimulated curvature in the dark. Unilateral application of Ca2+ to the elongation zone of intact roots or to the cut end of detipped roots caused either no curvature or very slight curvature toward the Ca2+. Thus, Ca2+ action on root elongation differs depending on its site of application. The stimulatory action of Ca2+ may involve an elevation of cytoplasmic Ca2+ in root cap cells and may partipate in root tropisms.

NASA Program Space Biology↗

NASA NTRS1988

Effects of cations on hormone transport in primary roots of Zea mays

We examined the influence of aluminum and calcium (and certain other cations) on hormone transport in corn roots. When aluminum was applied unilaterally to the caps of 15 mm apical root sections the roots curved strongly away from the aluminum. When aluminum was applied unilaterally to the cap and 3H-indole-3-acetic acid was applied to the basal cut surface twice as much radioactivity (assumed to be IAA) accumulated on the concave side of the curved root as on the convex side. Auxin transport in the apical region of intact roots was preferentially basipetal, with a polarity (basipetal transport divided by acropetal transport) of 6.3. In decapped 5 mm apical root segments, auxin transport was acropetally polar (polarity = 0.63). Application of aluminum to the root cap strongly promoted acropetal transport of auxin reducing polarity from 6.3 to 2.1. Application of calcium to the root cap enhanced basipetal movement of auxin, increasing polarity from 6.3 to 7.6. Application of the calcium chelator, ethylene-glycol-bis-(beta-aminoethylether)-N,N,N',N'-tetraacetic acid, greatly decreased basipetal auxin movement, reducing polarity from 6.3 to 3.7. Transport of label after application of tritiated abscisic acid showed no polarity and was not affected by calcium or aluminum. The results indicate that the root cap is particularly important in maintaining basipetal polarity of auxin transport in primary roots of corn. The induction of root curvature by unilateral application of aluminum or calcium to root caps is likely to result from localized effects of these ions on auxin transport. The findings are discussed relative to the possible role of calcium redistribution in the gravitropic curvature of roots and the possibility of calmodulin involvement in the action of calcium and aluminum on auxin transport.

NASA Discipline Plant Biology↗