scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
TL;DR: The proposed branch and bound type algorithm attains finiteε-convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems.
Abstract: A branch and bound global optimization method,αBB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convex relaxation of the original nonconvex problem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the α parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finitee-convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method,αBB, is implemented in C and tested on a variety of example problems.

442 citations

Journal ArticleDOI
TL;DR: In this article, a rigorous mathematical formulation for the problem of optimal design under uncertainty is presented, which involves a nonlinear infinite programming problem in which an optimization is performed on the set of design and control variables, such that the inequality constraints of the chemical plant are satisfied for every parameter value that belongs to a specified polyhedral region.
Abstract: A rigorous mathematical formulation is presented for the problem of optimal design under uncertainty. This formulation involves a nonlinear infinite programming problem in which an optimization is performed on the set of design and control variables, such that the inequality constraints of the chemical plant are satisfied for every parameter value that belongs to a specified polyhedral region. To circumvent the problem of infinite dimensionality in the constraints, an equivalence for the feasibility condition is established which leads to a max-min-max constraint. It is shown that if the inequalities are convex, only the vertices in the polyhedron need to be considered to satisfy this constraint. Based on this feature, an algorithm is proposed which uses only a small subset of the vertices in an iterative multiperiod design formulation. Examples are presented to illustrate the application to flexible design problems.

439 citations

Journal ArticleDOI
TL;DR: An improved algorithm for simultaneous strategies for dynamic optimization based on interior point methods is developed and a reliable and efficient algorithm to adjust elements to track optimal control profile breakpoints and to ensure accurate state and control profiles is developed.

438 citations

ReportDOI
01 Dec 1983
TL;DR: MINOS is a large-scale optimization system, for the solution of sparse linear and nonlinear programs, with features including a new basis package, automatic scaling of linear constraints, and automatic estimation of some or all gradients.
Abstract: : MINOS is a large-scale optimization system, for the solution of sparse linear and nonlinear programs. The objective function and constraists may be linear or nonlinear, or a mixture of both. The nonlinear functions must be smooth. Stable numerical methods are employed throughout. Features include a new basis package(for maintaining sparse LU factors of the basis matrix), automatic scaling of linear constraints, and automatic estimation of some or all gradients. Upper and lower bounds on the variables are handled efficiently. File formats for constraint and basis data are compatible with the industry MPS format. The source code is suitable for machines with a Fortran 66 or 77 compiler and at least 500K bytes of storage. (Author)

438 citations

Journal ArticleDOI
TL;DR: In this article, a nonlinear mixed-integer programming with inter-temporal constraints is proposed to solve the problem of virtual power plant (VPP) bidding in a joint market of energy and spinning reserve service.
Abstract: This paper addresses the bidding problem faced by a virtual power plant (VPP) in a joint market of energy and spinning reserve service. The proposed bidding strategy is a non-equilibrium model based on the deterministic price-based unit commitment (PBUC) which takes the supply-demand balancing constraint and security constraints of VPP itself into account. The presented model creates a single operating profile from a composite of the parameters characterizing each distributed energy resources (DER), which is a component of VPP, and incorporates network constraints into its description of the capabilities of the portfolio. The presented model is a nonlinear mixed-integer programming with inter-temporal constraints and solved by genetic algorithm (GA).

433 citations


Network Information
Related Topics (5)
Optimization problem
96.4K papers, 2.1M citations
93% related
Scheduling (computing)
78.6K papers, 1.3M citations
86% related
Robustness (computer science)
94.7K papers, 1.6M citations
86% related
Linear system
59.5K papers, 1.4M citations
85% related
Control theory
299.6K papers, 3.1M citations
84% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023113
2022259
2021615
2020650
2019640
2018630