Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Exact penalty”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

7 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

An infeasible-start framework for convex quadratic optimization, with application to constraint-reduced interior-point and other methods

A framework is proposed for solving general convex quadratic programs (CQPs) from an infeasible starting point by invoking an existing feasible-start algorithm tailored for inequality-constrained CQPs. The central tool is an exact penalty function scheme equipped with a penalty-parameter updating rule. The feasible-start algorithm merely has to satisfy certain general requirements, and so is the updating rule. Under mild assumptions, the framework is proved to converge on CQPs with both inequality and equality constraints and, at a negligible additional cost per iteration, produces an infeasibility certificate, together with a feasible point for an (approximately) ℓ 1 -least relaxed feasible problem, when the given problem does not have a feasible solution. The framework is applied to a feasible-start constraint-reduced interior-point algorithm previously proved to be highly performant on problems with many more inequality constraints than variables (“imbalanced”). Numerical comparison with popular codes (OSQP, qpOASES, MOSEK) is reported on both randomly generated problems and support-vector machine classifier training problems. The results show that the former typically outperforms the latter on imbalanced problems. Finally, application of the proposed infeasible-start framework to other feasible-start algorithms is briefly considered, and is tested on a simplex iteration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An adaptive stochastic sequential quadratic programming with differentiable exact augmented lagrangians

In this study, we consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global "almost sure" convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Two methods to study inelastic neutron-scattering measurements based on ω n (q) versus S(q, ω) applied to the magnetic open honeycomb lattice Tb 2 Ir 3 Ga 9

This work describes two methods to fit the inelastic neutron-scattering spectrum S(q, ω) with wavevector q and frequency ω. The common and well-established method extracts the experimental spin-wave branches ω n (q) from the measured spectra S(q, ω) and then minimizes the difference between the observed and predicted frequencies. When n branches of frequencies are predicted but the measured frequencies overlap to produce only m < n branches, the weighted average of the predicted frequencies must be compared to the observed frequencies. A penalty is then exacted when the width of the predicted frequencies exceeds the width of the observed frequencies. The second method directly compares the measured and predicted intensities S(q, ω) over a grid {q i , ω j } in wavevector and frequency space. After subtracting background noise from the observed intensities, the theoretical intensities are scaled by a simple wavevector-dependent function that reflects the instrumental resolution. Furthermore, the advantages and disadvantages of each approach are demonstrated by studying the open honeycomb material Tb 2 Ir 3 Ga 9 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

An Exact Algorithm for the Linear Tape Scheduling Problem

Magnetic tapes are often considered as an outdated storage technology, yet they are still used to store huge amounts of data. Their main interests are a large capacity and a low price per gigabyte, which come at the cost of a much larger file access time than on disks. With tapes, finding the right ordering of multiple file accesses is thus key to performance. Moving the reading head back and forth along a kilometer long tape has a non-negligible cost and unnecessary movements thus have to be avoided. However, the optimization of tape request ordering has rarely been studied in the scheduling literature, much less than I/O scheduling on disks. For instance, minimizing the average service time for several read requests on a linear tape remains an open question. Therefore, in this paper, we aim at improving the quality of service experienced by users of tape storage systems, and not only the peak performance of such systems. To this end, we propose a reasonable polynomial-time exact algorithm while this problem and simpler variants have been conjectured NP-hard. We also refine the proposed model by considering U-turn penalty costs accounting for inherent mechanical accelerations. Then, we propose a low-cost variant of our optimal algorithm by restricting the solution space, yet still yielding an accurate suboptimal solution. Finally, we compare our algorithms to existing solutions from the literature on logs of the mass storage management system of a major datacenter. This allows us to assess the quality of previous solutions and the improvement achieved by our low-cost algorithm. Aiming for reproducibility, we make available the complete implementation of the algorithms used in our evaluation, alongside the dataset of tape requests that is, to the best of our knowledge, the first of its kind to be publicly released.

Honoré, Valentin↗
DOE OSTI2025

Global stellarator coil optimization with quadratic constraints and objectives

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10$ 2 x faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL’s effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗