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Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.


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Journal ArticleDOI
TL;DR: It is shown that the problem variables, on the trajectory of minima of the sequence of unconstrained functions, can be developed as functions of a single parameter, which provides the theoretical basis for an extrapolation technique that significantly accelerates convergence in actual computations.
Abstract: In a previous article [Fiacco, A. V., G. P. McCormick. 1964. The sequential unconstrained minimization technique for nonlinear programming, a primal-dual method. Management Sci. 10(2) 360–366.] the authors gave the theoretical validation of the sequential unconstrained minimization technique for solving the convex programming problem. The technique is based on an idea proposed by C. W. Carroll [Carroll, C. W. 1961. The created response surface technique for optimizing nonlinear restrained systems. Oper. Res. 9(2) 169–184; Carroll, C. W. 1959. An operations research approach to the economic optimization of a Kraft Pulping Process. Doctoral dissertation, The Institute of Paper Chemistry, Appleton, Wisc.]. The method has been implemented via an algorithm based on a second-order gradient technique that has proved extremely efficient on a considerable number of test problems of varying complexity. This paper explores the computational aspects of the method. Included are discussions of parameter selection, conv...

185 citations

Journal ArticleDOI
TL;DR: A novel nonlinear neural network (NN) predictive control strategy based on the new tent-map chaotic particle swarm optimization (TCPSO) is presented to enhance the convergence and accuracy of the TCPSO.
Abstract: In this letter, a novel nonlinear neural network (NN) predictive control strategy based on the new tent-map chaotic particle swarm optimization (TCPSO) is presented. The TCPSO incorporating tent-map chaos, which can avoid trapping to local minima and improve the searching performance of standard particle swarm optimization (PSO), is applied to perform the nonlinear optimization to enhance the convergence and accuracy. Numerical simulations of two benchmark functions are used to test the performance of TCPSO. Furthermore, simulation on a nonlinear plant is given to illustrate the effectiveness of the proposed control scheme

185 citations

Journal ArticleDOI
TL;DR: Large-scale general (nonconvex) nonlinear programming when first and second derivatives of the objective and constraint functions are available is concerned, and a method suitable for large problems can be obtained.
Abstract: This paper concerns large-scale general (nonconvex) nonlinear programming when first and second derivatives of the objective and constraint functions are available. A method is proposed that is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved with a modified Newton method that generates search directions from a primal-dual system similar to that proposed for interior methods. The augmented penalty-barrier function may be interpreted as a merit function for values of the primal and dual variables. An inertia-controlling symmetric indefinite factorization is used to provide descent directions and directions of negative curvature for the augmented penalty-barrier merit function. A method suitable for large problems can be obtained by providing a version of this factorization that will treat large sparse indefinite systems.

184 citations

Book
16 Aug 1996
TL;DR: In this paper, the authors present a dynamic network model for urban transportation networks and propose a solution algorithm for an ideal route choice model based on the Frank-Wolfe algorithm, which solves the LP Subproblem.
Abstract: I Dynamic Transportation Network Analysis.- 1 Introduction.- 1.1 Requirements for Dynamic Modeling.- 1.2 Urban Transportation Network Analysis.- 1.3 Overview of Dynamic Network Models.- 1.4 Hierarchy of Dynamic Network Models.- 1.5 Notes.- II Mathematical Background.- 2 Variational Inequalities and Continuous Optimal Control.- 2.1 Variational Inequality Problems.- 2.1.1 Definitions.- 2.1.2 Existence and Uniqueness.- 2.1.3 Relaxation Algorithm.- 2.2 Continuous Optimal Control Problems.- 2.2.1 Definitions.- 2.2.2 No Constraints.- 2.2.3 Equality and Inequality Constraints.- 2.2.4 Equality and Nonnegativity Constraints.- 2.3 Hierarchical Optimal Control Problems.- 2.3.1 Static Two-Person Games.- 2.3.2 Dynamic Games.- 2.3.3 Bilevel Optimal Control Problems.- 2.4 Notes.- 3 Discrete Optimal Control and Nonlinear Programming.- 3.1 Discrete Optimal Control Problems.- 3.1.1 No Constraints.- 3.1.2 Equality and Inequality Constraints.- 3.1.3 Equality and Nonnegativity Constraints.- 3.2 Nonlinear Programming Problems.- 3.2.1 Unconstrained Minimization.- 3.2.2 General Constraints.- 3.2.3 Linear Equality and Nonnegativity Constraints.- 3.2.4 Discrete Optimal Control and Nonlinear Programs.- 3.3 Solution Algorithms.- 3.3.1 One Dimensional Minimization.- 3.3.2 Frank-Wolfe Algorithm.- 3.4 Notes.- III Deterministic Dynamic Route Choice.- 4 Network Flow Constraints and Definitions of Travel Times.- 4.1 Flow Conservation Constraints.- 4.2 Definitions.- 4.3 Flow Propagation Constraints.- 4.3.1 Type I.- 4.3.2 Type II.- 4.3.3 Type III.- 4.4 First-In-First-Out Constraints.- 4.5 Link Capacity and Oversaturation.- 4.5.1 Maximal Number of Vehicles on a Link.- 4.5.2 Maximal Exit Flow from a Link.- 4.5.3 Constraints for Spillback.- 4.6 Notes.- 5 Ideal Dynamic Route Choice Models.- 5.1 An Example with Two Parallel Routes.- 5.2 Definition of an Ideal State.- 5.3 A Route-Time-Based Model.- 5.3.1 Route-Time-Based Conditions.- 5.3.2 Dynamic Network Constraints.- 5.3.3 The Variational Inequality Problem.- 5.4 A Link-Time-Based Model.- 5.4.1 Link-Time-Based Conditions.- 5.4.2 The Variational Inequality Problem.- 5.5 A Numerical Example.- 5.6 A Multi-Class Route-Cost-Based Model.- 5.6.1 Multi-Class Route-Cost-Based Conditions.- 5.6.2 Dynamic Network Constraints.- 5.6.3 The Variational Inequality Problem.- 5.7 A Multi-Class Link-Cost-Based Model.- 5.7.1 Multi-Class Link-Cost-Based Conditions.- 5.7.2 The Variational Inequality Problem.- 5.8 Notes.- 6 A Solution Algorithm for an Ideal Route Choice Model.- 6.1 Statement of the Algorithm.- 6.1.1 Discrete VI Model for the Link-Time-Based Case.- 6.1.2 Relaxation Procedure and Optimization Problem.- 6.1.3 The Frank-Wolfe Method.- 6.2 Solving the LP Subproblem.- 6.3 Computational Experience.- 6.4 Notes.- 7 Instantaneous Dynamic Route Choice Models.- 7.1 Definition of an Instantaneous State.- 7.2 A Route-Time-Based Model.- 7.2.1 Route-Time-Based Conditions.- 7.2.2 Dynamic Network Constraints.- 7.2.3 The Variational Inequality Problem.- 7.3 A Link-Time-Based Model.- 7.3.1 Link-Time-Based Conditions.- 7.3.2 The Variational Inequality Problem.- 7.4 Solution Algorithm.- 7.4.1 Discrete VI Model for the Link-Time-Based Case.- 7.4.2 Relaxation Procedure and Optimization Program.- 7.4.3 The Frank-Wolfe Method.- 7.4.4 Numerical Example.- 7.5 Notes.- 8 Extensions of Instantaneous Route Choice Models.- 8.1 Optimal Control Model 1.- 8.1.1 Model Formulation.- 8.1.2 Optimality Conditions.- 8.1.3 DUO Equivalence Analysis.- 8.2 Optimal Control Model 2.- 8.2.1 Model Formulation.- 8.2.2 Optimality Conditions.- 8.3 A Multi-Class Route-Cost-Based Model.- 8.3.1 Multi-Class Route-Cost-Based Conditions.- 8.3.2 Dynamic Network Constraints.- 8.3.3 The Variational Inequality Problem.- 8.4 A Multi-Class Link-Cost-Based Model.- 8.4.1 Multi-Class Link-Cost-Based Conditions.- 8.4.2 The Variational Inequality Problem.- 8.5 Notes.- IV Stochastic Dynamic Route Choice.- 9 Ideal Stochastic Dynamic Route Choice Models.- 9.1 Redefinition of Dynamic Travel Times.- 9.2 Formulation of the Model.- 9.2.1 Network Constraints.- 9.2.2 Stochastic Route Choice and the Ideal SDUO State.- 9.2.3 Two Popular Route Choice Functions.- 9.2.4 Ideal Route Choice Conditions and VI Problem.- 9.2.5 Analysis of Dispersed Route Choice.- 9.3 Solution Algorithm.- 9.3.1 The Discrete Variational Inequality Problem.- 9.3.2 The Relaxation Method.- 9.3.3 Method of Successive Averages.- 9.3.4 Summary of the Solution Algorithm.- 9.3.5 A Logit-Based Ideal Stochastic Loading.- 9.3.6 Proof of the Algorithm.- 9.4 Numerical Example.- 9.5 Notes.- 10 Instantaneous Stochastic Dynamic Route Choice Models.- 10.1 Formulation of the Model.- 10.1.1 Network Constraints.- 10.1.2 Definition of an Instantaneous SDUO State.- 10.1.3 Instantaneous Route Choice Conditions and VI Problem.- 10.2 Solution Algorithm.- 10.2.1 The Discrete Variational Inequality Problem.- 10.2.2 The Relaxation Method.- 10.2.3 Method of Successive Averages.- 10.2.4 Summary of the Solution Algorithm.- 10.2.5 A Logit-Based Instantaneous Stochastic Loading.- 10.2.6 Proof of the Algorithm.- 10.3 An Instantaneous Optimal Control Model.- 10.4 Numerical Example.- 10.5 Notes.- V General Dynamic Travel Choices.- 11 Combined Departure Time/Route Choice Models.- 11.1 Additional Network Constraints.- 11.2 A Route-Based Model.- 11.2.1 Route-Based Conditions.- 11.2.2 Dynamic Network Constraints.- 11.2.3 The Variational Inequality Problem.- 11.3 A Link-Based Model.- 11.3.1 Link-Based Conditions.- 11.3.2 The Variational Inequality Problem.- 11.4 Solution Algorithm and An Example.- 11.4.1 Discrete Variational Inequality Problem.- 11.4.2 Relaxation Procedure and Optimization Problem.- 11.4.3 Numerical Example.- 11.5 Notes.- 12 Combined Mode/Departure Time/Route Choice Models.- 12.1 The Combined Travel Choice Problem.- 12.2 Individual Travel Choice Problems.- 12.2.1 Mode Choice Problem.- 12.2.2 Departure Time/Route Choice for Motorists.- 12.3 The Link-Time-Based Model.- 12.3.1 Network Constraints.- 12.3.2 The Variational Inequality Problem.- 12.4 Notes.- VI Implications for ITS.- 13 Link Travel Time Functions for Dynamic Network Models.- 13.1 Functions for Various Purposes.- 13.2 Stochastic Link Travel Time Functions.- 13.2.1 Moving Queue Concept.- 13.2.2 Cruise Time.- 13.2.3 Delay and Link Travel Time Functions.- 13.3 Deterministic Link Travel Time Functions.- 13.4 Implications of the Proposed Functions.- 13.4.1 Number of Link Flow Variables.- 13.4.2 Physical Constraints for Link Traffic Flow.- 13.4.3 Notes on Functions for Arterial Links.- 13.5 Functions for Freeway Segments.- 13.6 Notes.- 14 Implementation in Intelligent Transportation Systems.- 14.1 Implementation Issues.- 14.1.1 Traffic Prediction.- 14.1.2 Dynamic Route Guidance.- 14.1.3 Integrated Traffic Control/Information System.- 14.1.4 Incident Management.- 14.1.5 Congestion Pricing.- 14.1.6 Operations and Control for AHS.- 14.1.7 Transportation Planning.- 14.2 Practical Considerations.- 14.2.1 Rolling Horizon Implementation.- 14.2.2 Traveler Knowledge of Information.- 14.2.3 Response to Current and Anticipated Conditions.- 14.2.4 Flow-Based vs. Vehicle-Based Models.- 14.2.5 Different Types of Travelers.- 14.3 Data Requirements.- 14.3.1 Time-Dependent O-D Matrices.- 14.3.2 Network Geometry and Control Data.- 14.3.3 Traffic Flow Data.- 14.3.4 Traveler Information.- 14.4 Notes.- References.- Author Index.- List of Figures.- List of Tables.

184 citations

Journal ArticleDOI
TL;DR: By integrating a GA with a nonlinear interior point method (IPM), a novel hybrid method for the optimal reactive power flow (ORPF) problem is proposed in this article, which can be mainly divided into two parts.
Abstract: By integrating a genetic algorithm (GA) with a nonlinear interior point method (IPM), a novel hybrid method for the optimal reactive power flow (ORPF) problem is proposed in this paper. The proposed method can be mainly divided into two parts. The first part is to solve the ORPF with the IPM by relaxing the discrete variables. The second part is to decompose the original ORPF into two sub-problems: continuous optimization and discrete optimization. The GA is used to solve the discrete optimization with the continuous variables being fixed, whereas the IPM solves the continuous optimization with the discrete variables being constant. The optimal solution can be obtained by solving the two sub-problems alternately. A dynamic adjustment strategy is also proposed to make the GA and the IPM to complement each other and to enhance the efficiency of the hybrid proposed method. Numerical simulations on the IEEE 30-bus, IEEE 118-bus and Chongqing 161-bus test systems illustrate that the proposed hybrid method is efficient for the ORPF problem

184 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023113
2022259
2021615
2020650
2019640
2018630