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Parameter optimization using the L_∞ exact penalty function and strictly convex quadratic programming problems

APPLIED MATHEMATICS AND COMPUTATION 2008年第2期198卷 833-848页

作者： Fabien, Brian C. Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents an algorithm for the numerical solution of constrained parameter optimization problems. The solution strategy is based on a sequential quadratic programming (SQP) technique that uses the L-infinity exact penalty function. Unlike similar SQP algorithms the method proposed here solves only strictly convex quadratic programs to obtain the search directions. The global convergence properties of the algorithm are enhanced by the use of a nonmonotone line search and second-order corrections to avoid the Maratos effect. The paper also presents an ANSI C implementation of the algorithm. The effectiveness of the proposed method is demonstrated by solving numerous parameter optimization and optimal control problems that have appeared in the literature. (C) 2007 Elsevier Inc. All rights reserved.

关键词： nonlinear programming problem sequential quadratic programming convex quadratic programming computer code

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A robust pseudospectral method for numerical solution of nonlinear optimal control problems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2021年第6期98卷 1146-1165页

作者： Mehrpouya, Mohammad Ali Peng, Haijun Tafresh Univ Dept Math Tafresh *** Iran Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dept Engn Mech Dalian Peoples R China

In the present paper, a robust pseudospectral method for efficient numerical solution of nonlinear optimal control problems is presented. In the proposed method, at first, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality which are led to the Hamiltonian boundary value problem are derived. Then, utilizing a pseudospectral method for discretization, the nonlinear optimal control problem is converted to a system of nonlinear algebraic equations. However, the need to have a good initial guess may lead to a challenging problem for solving the obtained system of nonlinear equations. So, an optimization approach is introduced to simplify the need of a good initial guess. Numerical findings of some benchmark examples are presented at the end and computational features of the proposed method are reported.

关键词： Optimal control Hamiltonian boundary value problem Pontryagin's minimum principle pseudospectral methods nonlinear programming problem

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Optimization method for solving bang-bang and singular control problems

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控制理论与应用（英文版） 2012年第4期10卷 559-564页

作者： Shurong LI Ruiyan ZHAO Qiang ZHANG College of Information and Control Engineering China University of Petroleum

In this paper we study optimal control problems with the control variable appearing linearly. A novel method for optimization with respect to the switching times of controls containing both bang-bang and singular arcs is presented. This method transforms the control problem into a finite-dimensional optimization problem by reformulating the control problem as a multi-stage optimization problem. The optimal control problem is partitioned as several stages, with each stage corresponding to a particular control arc. A control vector parameterization approach is applied to convert the control problem to a static nonlinear programming （NLP） problem. The control profiles and stage lengths act as decision variables. Based on the Pontryagin maximal principle, a multi-stage adjoint system is constructed to calculate the gradients required by the NLP solvers. Two examples are studied to demonstrate the effectiveness of this strategy.

关键词： Bang-bang control Singular control Multi-stage problem nonlinear programming problem

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Risk-constrained offering strategies for a large-scale price-maker electric vehicle demand aggregator

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IET SMART GRID 2020年第6期3卷 860-869页

作者： Hossein Abbasi, Mohammad Taki, Mehrdad Rajabi, Amin Li, Li Zhang, Jiangfeng Univ Qom Dept Elect Engn Qom Iran Univ Technol Dept Elect & Data Engn Sydney NSW Australia Clemson Univ Dept Automot Engn Clemson SC 29631 USA

In this study, the problem of an electric vehicle (EV) aggregator participating in a three-settlement pool-based market is presented. In addition to energy procurement, it is assumed that EVs can sell electricity back to the markets. In order to obtain optimised solutions, the aggregator is considered as a price-maker agent who tries to minimise the cost of purchasing energy from the markets by offering price-energy bids in the day-ahead market and only energy bids in both adjustment and balancing markets. Since the problem is heavily constrained by equality constraints, the number of binary variables for a 24-hour market horizon is too large which leads to intractability when solved by traditional mathematical algorithms like the interior point. Therefore, an evolutionary metaheuristic algorithm based on genetic algorithms (GAs) is proposed to deal with the intractability. In this regard, first, the stochastic problem is formulated as a mixed-integer linear programming problem, and as a non-linear programming problem to be solved by CPLEX and GA, respectively. The former is used to ensure that the GA is tuned properly, and helps to avoid converging to local extremums. Furthermore, the solutions of the two formulations are compared in simulations to demonstrate GA could be faster in obtaining better results.

关键词： power generation economics genetic algorithms pricing linear programming optimisation power markets integer programming 24-hour market horizon intractability traditional mathematical algorithms evolutionary metaheuristic algorithm genetic algorithms stochastic problem mixed-integer linear programming problem nonlinear programming problem risk-constrained offering strategies large-scale price-maker electric vehicle demand aggregator electric vehicle aggregator EV three-settlement pool-based market energy procurement electricity optimised solutions price-maker agent purchasing energy price-energy bids day-ahead market balancing markets

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Numerical optimal control applied to an epidemiological model

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IFAC-PapersOnLine 2018年第2期51卷 1-6页

作者： Schreppel, Christina Chudej, Kurt Wessling82234 Germany Chair of Scientific Computing University of Bayreuth Bayreuth95440 Germany

A previously published SIR-ASI optimal control model of dengue fever is described and the optimal control problem is solved in this paper by an alternative solution approach, namely by a direct transcription method. In this method, the optimal control problem is substituted by a nonlinear programming problem. The nonlinear programming problem is solved by an interior point method. In the following an a posteriori check of the necessary optimality conditions of optimal control, which has not yet been done, is performed with the discretized states, adjoints, and controls. The check shows some accordance with the numerical results, but unfortunately in this setting a seldom discrepancy is observed, which seems to be connected with the modeling of the mechanical control. © 2018

关键词： nonlinear programming Insecticides Optimal control systems Transcription Dengue fevers Direct transcription method Epidemiological modeling Mechanical control Necessary optimality condition nonlinear programming problem Numerical results Optimal controls

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PARAMETER OPTIMIZATION problemS FOR MULTILAYER OPTICAL COATINGS

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CYBERNETICS AND SYSTEMS ANALYSIS 2005年第4期41卷 564-571页

作者： Stetsyuk, P. I. Mitsa, A. A. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine Uzhgorod Natl Univ Uzhgorod Ukraine

Two problems of finding optimal parameters for multilayer optical coatings are considered. They are formulated as multiextremal nonlinear programming problems with a complex objective function. Finding local extrema by first-order methods is discussed. The ways of calculating the gradient of the objective function depending on the number of layers in the optical coating are analyzed.

关键词： multilayer optical coating characteristic matrix radiation transmission factor nonlinear programming problem gradient method

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On the Radau pseudospectral method: theoretical and implementation advances

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CEAS SPACE JOURNAL 2017年第3期9卷 313-331页

作者： Sagliano, Marco Theil, Stephan Bergsma, Michiel D'Onofrio, Vincenzo Whittle, Lisa Viavattene, Giulia Deutsch Zentrum Luft & Raumfahrt Robert Hooke Str 7 Bremen Germany

In the last decades the theoretical development of more and more refined direct methods, together with a new generation of CPUs, led to a significant improvement of numerical approaches for solving optimal-control problems. One of the most promising class of methods is based on pseudospectral optimal control. These methods do not only provide an efficient algorithm to solve optimalcontrol problems, but also define a theoretical framework for linking the discrete numerical solution to the analytical one in virtue of the covector mapping theorem. However, several aspects in their implementation can be refined. In this framework SPARTAN, the first European tool based on flipped-Radau pseudospectral method, has been developed. This paper illustrates the aspects implemented for SPARTAN, which can potentially be valid for any other transcription. The novelties included in this work consist specifically of a new hybridization of the Jacobian matrix computation made of four distinct parts. These contributions include a new analytical formulation for expressing Lagrange cost function for open final-time problems, and the use of dual-number theory for ensuring exact differentiation. Moreover, a self-scaling strategy for primal and dual variables, which combines the projected-Jacobian rows normalization and the covector mapping, is described. Three concrete examples show the validity of the novelties introduced, and the quality of the results obtained with the proposed methods.

关键词： Pseudospectral methods Optimal control nonlinear programming problem SPARTAN

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Optimisation of the duplex D2D network: a deep learning approach

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IET NETWORKS 2020年第3期9卷 139-144页

作者： Liu, Xian Univ Arkansas Little Rock Dept Syst Engn Little Rock AR 72204 USA

For wireless networks, it is highly desirable to design a quality-of-service-promotion strategy to allocate the transmission power. In this study, the authors apply the deep learning methodology to solve such a problem in a duplex device-to-device network. The model is formulated as a constrained non-linear programming problem. The training data are generated by a standard optimisation tool. Then, an artificial neural network is designed to learn the system from the training data. Simulation results show the effectiveness of deep leaning.

关键词： learning (artificial intelligence) neural nets optimisation nonlinear programming linear programming cellular radio duplex D2D network deep learning approach wireless networks quality-of-service-promotion strategy transmission power deep learning methodology device-to-device network nonlinear programming problem training data standard optimisation tool artificial neural network deep leaning

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Model-Based Optimal Experiment Design for nonlinear Parameter Estimation Using Exact Confidence Regions

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IFAC-PapersOnLine 2017年第1期50卷 13760-13765页

作者： Gottu Mukkula, Anwesh Reddy Paulen, Radoslav Process Dynamics and Operations Group Technische Universität Dortmund Germany

Optimal experiment design is usually performed as a search over a finitely-parameterized shape that (over-) approximates the confidence region of parameters of a model. In general, there exists no such shape to exactly enclose the confidence region of a nonlinear parameter estimation problem. Due to this fact, the design-of-experiment techniques are not well established for this problem and approximate designs are conducted. In this contribution, assuming Gaussian (normally distributed) noise, we propose and study (a) two schemes to over-approximate the confidence region of parameters using an ellipsoid and an orthotope and (b) a framework for optimal experiment design. We formulate the over-approximation of the confidence region as an optimization problem. The optimal experiment design is then proposed as a bi-level optimization problem. In line with the existing optimal experiment design methodology for a linear parameter estimation problem, we also propose several design criteria that optimize some measure of the over-approximated confidence region for the nonlinear case. The proposed bi-level optimization problem is solved (i) as a nonlinear programming problem using the necessary conditions for optimality or (ii) as a nested problem with globally optimized inner-level problem. We illustrate the proposed schemes on a benchmark test case. © 2017

关键词： Parameter estimation Benchmarking Design Design of experiments Mathematical programming nonlinear analysis nonlinear programming Normal distribution Statistics Bi level optimization problems Design of experiment techniques (DoE) Least squares estimation nonlinear Parameter Estimation nonlinear programming problem Optimal controls Optimal experiment design Optimization problems

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Efficient Partial Condensing Algorithms for nonlinear Model Predictive Control with Partial Sensitivity Update

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IFAC-PapersOnLine 2018年第20期51卷 406-411页

作者： Chen, Yutao Frison, Gianluca van Duijkeren, Niels Bruschetta, Mattia Beghi, Alessandro Diehl, Moritz Department of Information Engineering University of Padova Italy University of Freiburg Germany Department of Mechanical Engineering LeuvenKU United Kingdom

In nonlinear Model Predictive Control(NMPC), an optimal control problem (OCP) is solved repeatedly at every sampling instant. To satisfy the real-time restriction, modern methods tend to convert the OCP into structured nonlinear programming problems (NLP), which are approximately solved on-line. Real-Time Iteration is one of the promising NMPC algorithms that solves the NLP using a single Sequential Quadratic programming (SQP) iteration. To solve Quadratic programming (QP) problems efficiently, recently proposed partial condensing techniques reformulate large and sparse QP problems into smaller but still sparse ones. In this paper, we propose two tailored partial condensing algorithms by combining partial sensitivity updating schemes, that are recently proposed to update part of the sensitivities of dynamics. We show that such a combination can significantly reduce the computational time for partial condensing and for the full RTI step. © 2018

关键词： Model predictive control Iterative methods nonlinear systems Optimal control systems Predictive control systems Quadratic programming Real time control Structured programming Computational time nonlinear model predictive control nonlinear programming problem Numerical optimizations Optimal control problem Real time implementations Sampling instants Sequential quadratic programming

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