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Results for “Nonsmooth optimization”

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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Optimization-based design of control systems for flexible structures

The purpose of this presentation is to show that it is possible to use nonsmooth optimization algorithms to design both closed-loop finite dimensional compensators and open-loop optimal controls for flexible structures modeled by partial differential equations. An important feature of our approach is that it does not require modal decomposition and hence is immune to instabilities caused by spillover effects. Furthermore, it can be used to design control systems for structures that are modeled by mixed systems of coupled ordinary and partial differential equations.

Polak, E.↗
DOE OSTI2022

Interactive Exploration of High-Dimensional Phase Diagrams

High-dimensional thermodynamic phase stability databases are becoming increasingly common due to the convergence of three recent trends: (i) the widespread interest in so-called “high-entropy” alloys, (ii) the availability of high-throughput computational assessments of phase stability in broad composition spaces and (iii) the ongoing development of ever-increasingly broad, multicomponent, multiphase CALPHAD databases. Although automated computational tools can readily process such high-dimensional data, scientists are often unable to visualize the relevant phase relations, an ability that is crucial to gaining an intuitive understanding of the stability constraints governing materials design. The present work addresses this need by providing algorithms that enable the interactive exploration of phase equilibria in high-dimensional spaces. These algorithms concentrate the complex nonlinear nonsmooth optimization needed into a preprocessing step that generates a large number of high-dimensional yet elementary graphical primitives. Furthermore, these primitives can then be cross-sectioned to yield 3-dimensional views in a computationally efficient manner that enables an interactive exploration of high-dimensional spaces. All of these operations are highly parallelizable, thus facilitating scaling of this method to large data sets.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Randomized Federated Learning Methods for Nonsmooth, Nonconvex, and Hierarchical Optimization (Final Technical Report)

This final technical report summarizes the outcomes of a DOE-funded project on federated scientific machine learning (FL) under nonsmooth, nonconvex, and hierarchical optimization settings. The project develops new mathematical models, algorithms, and theoretical guarantees for decentralized stochastic, bilevel, and minimax optimization problems arising in DOE mission-relevant applications. A unified framework of randomized and zeroth-order federated optimization methods is introduced, providing provable convergence, communication efficiency, and sample-complexity guarantees. The report documents algorithmic design, theoretical analysis, and empirical validation of the proposed federated learning methods. The project also contributes to workforce development through graduate training and dissemination of results via publications and seminars.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- \({\boldsymbol{\mathcal{C}^2}}\) Objective

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objective functions is proposed and analyzed. Upper- \({\boldsymbol{\mathcal{C}^2}}\) is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- \({\boldsymbol{\mathcal{C}^2}}\) problems and a real-world optimal power flow problem used in current power grid industry practices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Linear convergence of accelerated conditional gradient algorithms in spaces of measures

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding coefficients. Under general assumptions, a sub-linear [see formula in PDF] rate in the objective functional is obtained, which is sharp in most cases. To improve efficiency, one can fully resolve the finite-dimensional subproblems occurring in each iteration of the method. We provide an analysis for the resulting procedure: under a structural assumption on the optimal solution, a linear [see formula in PDF] convergence rate is obtained locally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization

In many applications, one can only access the inexact gradients and inexact hessian times vector products. Thus it is essential to consider algorithms that can handle such inexact quantities with a guaranteed convergence to solution. An inexact adaptive and provably convergent semismooth Newton method is considered to solve constrained optimization problems. In particular, dynamic optimization problems, which are known to be highly expensive, are the focus. A memory efficient semismooth Newton algorithm is introduced for these problems. The source of efficiency and inexactness is the randomized matrix sketching. Further, applications to optimization problems constrained by partial differential equations are also considered.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Efficient proximal subproblem solvers for a nonsmooth trust-region method

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Genetic algorithm-based geometry calibration for dynamic compression x-ray diffraction experiments

An important component of dynamic compression x-ray diffraction (XRD) experiment analysis is geometry calibration: proper data interpretation requires knowledge of the precise detector position and orientation and, if the experiment involves a single-crystal sample, knowledge of the lattice orientation. The determination of these parameters in the arbitrary three-dimensional (3D) scattering geometries often present in dynamic compression facilities is challenging, as the associated optimization problem can be highly nonlinear, nonsmooth, and discontinuous. We present a genetic algorithm-based approach for performing dynamic compression XRD calibrations that overcomes these obstacles. We provide details regarding the image processing, algorithm implementation, and open-source software deployment and demonstrate the capability of the approach to calibrate the detector and crystal parameters in 3D geometries. Notably, we demonstrate the solver’s capacity to find the crystal orientation without a priori rotation constraints.

Brown, Nathan P. [Sandia National Laboratories (SN↗
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Supercomputer optimizations for stochastic optimal control applications

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

Chung, Siu-Leung↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
NASA NTRS1992

Active adhesion concepts for in-orbit structural construction

The in-orbit assembly of structural elements is presently addressed by means of a continuum-based theory of active-adhesion contact/impact which assumes the manufacturability of active adhesion elements by piezoelectric (and similarly behaving) materials. Block bonding characteristics can furnish an effective alternative to optimal control-based, impact surge force-mitigation strategies, especially in the numerous nonsmooth control problems that are difficult to synthesize and implement. Attention is given to design concepts employing combined serial/parallel-bonded active adhesion elements composed of cascaded piezoelectric devices.

Park, K. C.↗
NASA NTRS1994

Airfoil optimization by the one-shot method

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (Governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Language multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

Kuruvila, G.↗