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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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Proceedings ArticleDOI
08 Nov 1996
TL;DR: This talk discusses the stochastic counterpart (sample path) method where a relatively large sample is generated and the expected value function is approximated by the corresponding average function, and the obtained approximation problem is solved by deterministic methods of nonlinear programming.
Abstract: In this talk we consider a problem of optimizing an expected value function by Monte Carlo simulation methods. We discuss, somewhat in details, the stochastic counterpart (sample path) method where a relatively large sample is generated and the expected value function is approximated by the corresponding average function. Consequently the obtained approximation problem is solved by deterministic methods of nonlinear programming. One of advantages of this approach, compared with the classical stochastic approximation method, is that a statistical inference can be incorporated into optimization algorithms. This allows to develop a validation analysis, stopping rules and variance reduction techniques which in some cases considerably enhance numerical performance of the stochastic counterpart method.

156 citations

Journal ArticleDOI
TL;DR: Variations on the basic method for solving a general worst-case robust convex optimization problem that can give enhanced convergence, reduce data storage, or improve other algorithm properties are given.
Abstract: We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.

156 citations

Journal ArticleDOI
TL;DR: In this paper, a mixed-integer nonlinear programming approach is used to solve their optimal scheduling problems of energy systems in building integrated with energy generation and thermal energy storage in order to minimize the overall operation cost day-ahead.

156 citations

Journal ArticleDOI
TL;DR: A convex nonlinear relaxation of the nonlinear convex GDP problem that relies on the convex hull of each of the disjunctions that is obtained by variable disaggregation and reformulation of the inequalities is proposed.
Abstract: Generalized Disjunctive Programming (GDP) has been introduced recently as an alternative to mixed-integer programming for representing discrete/continuous optimization problems. The basic idea of GDP consists of representing these problems in terms of sets of disjunctions in the continuous space, and logic propositions in terms of Boolean variables. In this paper we consider GDP problems involving convex nonlinear inequalities in the disjunctions. Based on the work by Stubbs and Mehrotra [21] and Ceria and Soares [6], we propose a convex nonlinear relaxation of the nonlinear convex GDP problem that relies on the convex hull of each of the disjunctions that is obtained by variable disaggregation and reformulation of the inequalities. The proposed nonlinear relaxation is used to formulate the GDP problem as a Mixed-Integer Nonlinear Programming (MINLP) problem that is shown to be tighter than the conventional “big-M” formulation. A disjunctive branch and bound method is also presented, and numerical results are given for a set of test problems.

156 citations

Book
23 Apr 1993
TL;DR: In this paper, the authors present an approach for automated structural optimization using nonlinear programming and linear programming, with the objective of reducing the number of parameters to be used by the algorithm.
Abstract: 1 Problem Statement.- 1.1 Introduction.- 1.1.1 Automated Structural Optimization.- 1.1.2 Structural Optimization Methods.- 1.1.3 Historical Perspective.- 1.1.4 Scope of Text.- 1.2 Analysis Models.- 1.2.1 Elastic Analysis.- 1.2.2 Plastic Analysis.- 1.3 General Formulation.- 1.3.1 Design Variables.- 1.3.2 Constraints.- 1.3.3 Objective Function.- 1.3.4 Mathematical Formulation.- 1.4 Typical Problem Formulations.- 1.4.1 Displacement Method Formulations.- 1.4.2 Force Method Formulations.- Exercises.- 2 Optimization Methods.- 2.1 Optimization Concepts.- 2.1.1 Unconstrained Minimum.- 2.1.2 Constrained Minimum.- 2.2 Unconstrained Minimization.- 2.2.1 Minimization Along a Line.- 2.2.2 Minimization of Functions of Several Variables.- 2.3 Constrained Minimization: Linear Programming.- 2.3.1 Introduction.- 2.3.2 Problem Formulation.- 2.3.3 Method of Solution.- 2.3.4 Further Considerations.- 2.4 Constrained Minimization: Nonlinear Programming.- 2.4.1 Sequential Unconstrained Minimization.- 2.4.2 The Method of Feasible Directions.- 2.4.3 Other Methods.- Exercises.- 3 Approximation Concepts.- 3.1 General Approximations.- 3.1.1 Design Sensitivity Analysis.- 3.1.2 Intermediate Variables.- 3.1.3 Sequential Approximations.- 3.2 Approximate Behavior Models.- 3.2.1 Basic Displacement Approximations.- 3.2.2 Combined Displacement Approximations.- 3.2.3 Homogeneous Functions.- 3.2.4 Displacement Approximations along a Line.- 3.2.5 Approximate Force Models.- Exercises.- 4 Design Procedures.- 4.1 Linear Programming Formulations.- 4.1.1 Plastic Design.- 4.1.2 Elastic Design.- 4.2 Feasible-Design Procedures.- 4.2.1 General Considerations.- 4.2.2 Optimization in Design Planes.- 4.3 Optimality Criteria Procedures.- 4.3.1 Stress Criteria.- 4.3.2 Displacement Criteria.- 4.3.3 Design Procedures.- 4.3.4 The Relationship Between OC and MP.- 4.4 Multilevel Optimal Design.- 4.4.1 General Formulation.- 4.4.2 Two-Level Design of Prestressed Concrete Systems.- 4.4.3 Multilevel Design of Indeterminate Systems.- 4.5 Optimal Design and Structural Control.- 4.5.1 Optimal Control of Structures.- 4.5.2 Improved Optimal Design by Structural Control.- 4.6 Geometrical Optimization.- 4.6.1 Simultaneous Optimization of Geometry and Cross Sections.- 4.6.2 Approximations and Multilevel Optimization.- 4.7 Topological Optimization.- 4.7.1 Problem Statement.- 4.7.2 Types of Optimal Topologies.- 4.7.3 Properties of Optimal Topologies.- 4.7.4 Approximations and Two-Stage Procedures.- 4.8 Interactive Layout Optimization.- 4.8.1 Optimization Programs.- 4.8.2 Graphical Interaction Programs.- 4.8.3 Design Procedure.- Exercises.- References.

156 citations


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