Topic
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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TL;DR: The paper presents theory dealing primarily with properties of the relevant functions that result in convex programming problems, and discusses interpretations of this theory.
Abstract: This paper considers a class of optimization problems characterized by constraints that themselves contain optimization problems. The problems in the constraints can be linear programs, nonlinear programs, or two-sided optimization problems, including certain types of games. The paper presents theory dealing primarily with properties of the relevant functions that result in convex programming problems, and discusses interpretations of this theory. It gives an application with linear programs in the constraints, and discusses computational methods for solving the problems.
477 citations
TL;DR: A superstructure that has embedded many potential configurations of utility systems is proposed, as well as its corresponding mixed-integer programming model, for performing structural and parameter optimization in the synthesis of processing systems.
473 citations
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01 Oct 1987TL;DR: This paper presents a meta-modelling framework for solving the optimization problems that can be formulated as nonconvex quadratic problems and some of the methods used for solving these problems have been developed.
Abstract: Convex sets and functions.- Optimality conditions in nonlinear programming.- Combinatorial optimization problems that can be formulated as nonconvex quadratic problems.- Enumerative methods in nonconvex programming.- Cutting plane methods.- Branch and bound methods.- Bilinear programming methods for nonconvex quadratic problems.- Large scale problems.- Global minimization of indefinite quadratic problems.- Test problems for global nonconvex quadratic programming algorithms.
472 citations
TL;DR: An introductory survey of a class of optimization problems known as bilevel programming, which considers various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.
Abstract: This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.
471 citations
01 Jan 1986
TL;DR: NPSOL as discussed by the authors is a set of Fortran subroutines designed to minimize a smooth function subject to constraints, which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints.
Abstract: : This report forms the user's guide for Version 4.0 of NPSOL, a set of Fortran subroutines designed to minimize a smooth function subject to constraints, which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints. (NPSOL may also be used for unconstrained, bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and (optionally) their gradients. All matrices are treated as dense, and hence NPSOL is not intended for large sparse problems. NPSOL uses a sequential quadratic programming (SQP) algorithm, in which the search directions is the solution of a quadratic programming (QP) subproblem. The algorithm treats bounds, linear constraints and nonlinear constraints separately. The Hessian of each QP subproblem is a positive-definite quasi-Newton approximation to the Hessian of the Lagrangian function. The steplength at each iteration is required to produce a sufficient decrease an augmented Lagrangian merit function. Each QP subproblem is solved using a quadratic programming package with several features that improve the efficiency of an SQP algorithm. (Author)
471 citations