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.

Optimal Power Flow Using an Extended Conic Quadratic Formulation

Abstract: Recent research has shown that the load flow equations describing the steady-state conditions in a meshed network can be placed in extended conic quadratic (ECQ) format. This paper presents a study of the implementation of the new load flow equations format in an optimal power flow (OPF) program which accounts for control devices such as tap-changing transformers, phase-shifting transformers, and unified power flow controllers. The proposed OPF representation retains the advantages of the ECQ format: 1) it can be easily integrated within optimization routines that require the evaluation of second-order derivatives, 2) it can be efficiently solved for using primal-dual interior-point methods, and 3) it can make use of linear programming scaling techniques for improving numerical conditioning. The ECQ-OPF program is employed to solve the economic dispatch and active power loss minimization problems. Numerical testing is used to validate the proposed approach by comparing against solution methods and results of standard test systems.

Newton's Method for Generalized Equations.

Abstract: : Newton's method is a well known and often applied technique for computing a zero of a nonlinear function. By using the theory of generalized equations, a Newton method is developed to solve problems arising in both mathematical programming and mathematical economics. Two results concerning the convergence and convergence rate of Newton's method are proved for generalized equations. Examples are given to emphasize the application of this method to generalized equations representing the non-linear programming problem and the nonlinear complementarity problem. Computational results of Newton's method applied to a nonlinear complementarity problem of Kojima, and an invariant capital stock problem of Hansen and Koopmans are both presented.

Finite Algorithms in Optimization and Data Analysis

Abstract: Preface Table of Notation Some Results from Convex analysis Linear Programming Applications of linear Programming in Discrete Approximation Polyhedral Convex Functions Least Squares and Related Methods Some Applications to Non-Convex Problems Some Questions of Complexity and Performance Appendices References Index.

Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming

Abstract: We consider nonlinear programming problem P with stochastic constraints. The Lagrangean corresponding to such problems has a stochastic part, which in this work is replaced by its certainty equivalent in the sense of expected utility theory. It is shown that the deterministic surrogate problem CE-P thus obtained, contains a penalty function which penalizes violation of the constraints in the mean. The approach is related to several known methods in stochastic programming such as: chance constraints, stochastic goal programming, reliability programming and mean-variance analysis. The dual problem of CE-P is studied for problems with stochastic righthand sides in the constraints and a comprehensive duality theory is developed by introducing a new certainty equivalent NCE concept. Motivation for the NCE and its potential role in Decision Theory are discussed, as well as mean-variance approximations.

Distribution Systems Reconfiguration Based on OPF Using Benders Decomposition

Abstract: This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, load balancing among feeders, and is subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages, and radial optimal operation of networks. A specific approach of the generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages: the first one is the master problem and is formulated as a mixed integer nonlinear programming problem. This stage determines the radial topology of the distribution network. The second stage is the slave problem and is formulated as a nonlinear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in the general algebraic modeling system. The effectiveness of the proposal is demonstrated through three examples extracted from the literature.