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nonlinear programming methods for solving problems: A recent bibliographic review 4

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Nonlinear programming methods for solving problems: A recent...

4th International Conference on Chaotic Modeling and Simulation, CHAOS 2011

作者： Gavlak, Nícolas Fernando Gavlak, André Augusto Paulista University - UNIP Bauru Brazil Brazilian National Institute for Space Research - INPE São José dos Campos Brazil

A great number of mathematical-programming applications are cast naturally as linear programs. Linear programming assumptions or approximations may also lead to appropriate problem representations over the diversity of decision variables being measured. At other times, however, nonlinearities in the form of either nonlinear objective functions or nonlinear constraints are critical for representing an application properly as a mathematical program. In mathematics, nonlinear programming (NLP) is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear. This paper aims to list several nonlinear programming methods for solving problems that have been published at last 10 years. © 2019 CHAOS 2011 - 4th Chaotic Modeling and Simulation International Conference, Proceedings. All rights reserved.

关键词： nonlinear programming

An inexact projected gradient method with rounding and lifting by nonlinear programming for solving rank-one semidefinite relaxation of polynomial optimization

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arXiv 2021年

作者： Yang, Heng Liang, Ling Carlone, Luca Toh, Kim-Chuan Laboratory for Information and Decision Systems Massachusetts Institute of Technology Department of Mathematics National University of Singapore Department of Mathematics Institute of Operations Research and Analytics National University of Singapore

We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new algorithmic framework that blends local search using the nonconvex POP into global descent using the convex SDP. In particular, we first design a globally convergent inexact projected gradient method (iPGM) for solving the SDP that serves as the backbone of our framework. We then accelerate iPGM by taking long, but safeguarded, rank-one steps generated by fast nonlinear programming algorithms. We prove that the new framework is still globally convergent for solving the SDP. To solve the iPGM subproblem of projecting a given point onto the feasible set of the SDP, we design a two-phase algorithm with phase one using a symmetric Gauss-Seidel based accelerated proximal gradient method (sGS-APG) to generate a good initial point, and phase two using a modified limited-memory BFGS (L-BFGS) method to obtain an accurate solution. We analyze the convergence for both phases and establish a novel global convergence result for the modified L-BFGS that does not require the objective function to be twice continuously differentiable. We conduct numerical experiments for solving second-order SDP relaxations arising from a diverse set of POPs. Our framework demonstrates state-of-the-art efficiency, scalability, and robustness in solving degenerate rank-one SDPs to high accuracy, even in the presence of millions of equality *** Codes 90C06, 90C22, 90C23, 90C55 © 2021, CC BY.

关键词： nonlinear programming

NPASA: An algorithm for nonlinear programming - Motivation and global convergence

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arXiv 2021年

作者： Diffenderfer, James Hager, William W. Lawrence Livermore National Laboratory LivermoreCA United States The University of Florida GainesvilleFL United States

In this paper, we present a two phase method for solving nonlinear programming problems called nonlinear Polyhedral Active Set Algorithm (NPASA) that has global and local convergence guarantees under reasonable assumptions. The first phase consists of an augmented Lagrangian method to ensure global convergence while the second phase is designed to promote fast local convergence by performing a balanced reduction of two error estimators for nonlinear programs. After presenting error estimators for nonlinear programs and our algorithm NPASA, we establish global convergence properties for NPASA. Local quadratic convergence of NPASA is established in a companion paper [11]. © 2021, CC BY.

关键词： nonlinear programming

nonlinear programming approach to a shear-deformable hybrid beam element for large displacement analysis 7

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Nonlinear programming approach to a shear-deformable hybrid ...

7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2019

作者： Lyritsakis, Charilaos M. Andriotis, Charalampos P. Papakonstantinou, Konstantinos G. Pennsylvania State University University ParkPA16802 United States

ISBN: (纸本)9786188284456

In the present work, a hybrid beam element based on exact kinematics is developed, accounting for arbitrarily large displacements and rotations, as well as shear deformable cross sections. At selected quadrature points, fiber discretization of the cross sections facilitates efficient computation of the stress resultants for any uniaxial material law. The numerical approximation is carried out through the lens of nonlinear programming, where the enengy functional of the system is treated as the objective function and the exact strain-displacement relations form the set of kinematic constraints. The only interpolated field is curvature, whereas the centerline axial and shear strains, along with the displacement measures at the element edges, are determined by enforcing compatibility through the use of any preferable constrained optimization algorithm. The solution satisfying the necessary optimality conditions is determined by the stationary point of the Lagrangian. A set of numerical examples demonstrates the accuracy and performance of the proposed element against analytical or approximate solutions available in the literature. © 2019 The authors.

关键词： nonlinear programming

Coordinated receding-horizon control of battery electric vehicle speed and gearshift using relaxed mixed integer nonlinear programming

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arXiv 2021年

作者： Li, Nan Han, Kyoungseok Kolmanovsky, Ilya Girard, Anouck Department of Aerospace Engineering University of Michigan Ann ArborMI48109 United States School of Mechanical Engineering Kyungpook National University Daegu41566 Korea Republic of

In this paper, we propose an approach to coordinated receding-horizon control of vehicle speed and transmission gearshift for automated battery electric vehicles (BEVs) to achieve improved energy efficiency. The introduction of multispeed transmissions in BEVs creates an opportunity to manipulate the operating point of electric motors under given vehicle speed and acceleration command, thus providing the potential to further improve the energy efficiency. However, co-optimization of vehicle speed and transmission gearshift leads to a mixed integer nonlinear program (MINLP), solving which can be computationally very challenging. In this paper, we propose a novel continuous relaxation technique to treat such MINLPs that makes it possible to compute solutions with conventional nonlinear programming solvers. After analyzing its theoretical properties, we use it to solve the optimization problem involved in coordinated receding-horizon control of BEV speed and gearshift. Through simulation studies, we show that co-optimizing vehicle speed and transmission gearshift can achieve considerably greater energy efficiency than optimizing them sequentially, and the proposed relaxation technique can reduce the online computational cost to a level that is comparable to the time available for real-time implementation. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

Practical Methods for Optimal Control Using nonlinear programming, Third Edition

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丛书名： Advances in Design and Control

2020年

作者： John T. Betts

How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most effcient way to produce a chemical subst... 详细信息

ISBN: (数字)9781611976199

ISBN: (纸本)9781611976182

Practical Methods for Optimal Control Using nonlinear programming, Third Edition focuses on the direct transcription method for optimal control, and features

a summary of relevant material in constrained optimization, including nonlinear programming;
discretization techniques appropriate for ordinary differential equations and differential-algebraic equations; and
several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy.

The third edition has been thoroughly updated and includes

new material on implicit Runge–Kutta discretization techniques,
new chapters on partial differential equations and delay equations, and
more than 70 test problems and open source FORTRAN code for all of the problems.

This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.

关键词： Optimal control nonlinear programming ordinary differential equations differential-algebraic equations discretize then optimize

NPASA: An algorithm for nonlinear programming - Local convergence

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arXiv 2021年

作者： Diffenderfer, James Hager, William W. Lawrence Livermore National Laboratory LivermoreCA United States The University of Florida GainesvilleFL United States

In this paper, we provide local convergence analysis for the two phase nonlinear Polyhedral Active Set Algorithm (NPASA) designed to solve nonlinear programs. In particular, we establish local quadratic convergence of the primal iterates and global error estimator for NPASA under reasonable assumptions. Additionally, under the same set of assumptions we prove that only phase two of NPASA is executed after finitely many iterations. This paper is companion to a paper that provides motivation and global convergence analysis for NPASA [2]. © 2021, CC BY.

关键词： nonlinear programming

Scalable nonlinear programming framework for parameter estimation in dynamic biological system models

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PLOS COMPUTATIONAL BIOLOGY 2019年第3期15卷 e1006828-e1006828页

作者： Shin, Sungho Venturelli, Ophelia S. Zavala, Victor M. Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA Univ Wisconsin Dept Biochem 420 Henry Mall Madison WI 53705 USA

We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stiff differential equations as well as many experimental data sets and parameters. The proposed framework uses cutting-edge modeling and solution tools which are computationally efficient, robust, and easy-to-use. Specifically, our framework uses a time discretization approach that: i) avoids repetitive simulations of the dynamic model, ii) enables fully algebraic model implementations and computation of derivatives, and iii) enables the use of computationally efficient nonlinear interior point solvers that exploit sparse and structured linear algebra techniques. We demonstrate these capabilities by solving estimation problems for synthetic human gut microbiome community models. We show that an instance with 156 parameters, 144 differential equations, and 1,704 experimental data points can be solved in less than 3 minutes using our proposed framework (while an off-the-shelf simulation-based solution framework requires over 7 hours). We also create large instances to show that the proposed framework is scalable and can solve problems with up to 2,352 parameters, 2,304 differential equations, and 20,352 data points in less than 15 minutes. The proposed framework is flexible and easy-to-use, can be broadly applied to dynamic models of biological systems, and enables the implementation of sophisticated estimation techniques to quantify parameter uncertainty, to diagnose observability/uniqueness issues, to perform model selection, and to handle outliers. Author summary Constructing and validating dynamic models of biological systems spanning biomolecular networks to ecological systems is a challenging problem. Here we present a scalable computational framework to rapidly infer parameters in complex dynamic models of

关键词： nonlinear programming PARAMETER estimation BIOLOGICAL systems GUT microbiome DYNAMIC models COMPUTER simulation

Form-finding and analysis of hyperelastic tensegrity structures using unconstrained nonlinear programming

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ENGINEERING STRUCTURES 2019年 191卷 439-446页

作者： Arcaro, Vinicius Adeli, Hojjat Univ Estadual Campinas Coll Civil Engn Av Albert Einstein 951 BR-13083852 Campinas SP Brazil Ohio State Univ Dept Civil Environm & Geodet Engn 470 Hitchcock Hall2070 Neil Ave Columbus OH 43210 USA

This study presents a method for form-finding and analysis of hyperelastic tensegrity structures based on a special strut finite element and unconstrained nonlinear programming. The strut element can function as a hyperelastic truss element with an initial cut in its undeformed length or as a strut element that shows constant force irrespectively of its nodal displacements. For the hyperelastic strut element, the invariants of the Right Cauchy-Green deformation tensor are written in terms of the element's nodal displacements and the cut in the element's undeformed length. The structure's total potential energy is expressed as function of its nodal displacements and the cuts in the elements' undeformed lengths. The minimization of this function is a nonlinear programming problem where the displacements are the unknowns. The form-finding procedure is performed by a static analysis where the stiffness matrix maybe singular along the path to equilibrium without causing convergence problems. The mathematical model includes the element's cross-sectional deformation while the element moves in space, fully modelling its three-dimensional character. The constraint for incompressibility is satisfied exactly, eliminating the need for a penalty or augmented Lagrangian method.

关键词： Finite element Hyperelasticity Incompressibility Minimization nonlinear programming Quasi-Newton Tensegrity