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: In this paper, a generalized canonical nonlinear programming circuit (G-NPC) was proposed to solve a general class of nonsmooth non-linear programming problems, where the objective function and constraints are assumed to satisfy only the weak condition of being regular functions.
Abstract: In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time nonlinear programming problems where the objective function and the constraints are smooth (twice continuously differentiable) functions. In this paper, a generalized circuit is introduced (G-NPC), which is aimed at solving in real time a much wider class of nonsmooth nonlinear programming problems where the objective function and the constraints are assumed to satisfy only the weak condition of being regular functions. G-NPC, which derives from a natural extension of NPC, has a neural-like architecture and also features the presence of constraint neurons modeled by ideal diodes with infinite slope in the conducting region. By using the Clarke's generalized gradient of the involved functions, G-NPC is shown to obey a gradient system of differential inclusions, and its dynamical behavior and optimization capabilities, both for convex and nonconvex problems, are rigorously analyzed in the framework of nonsmooth analysis and the theory of differential inclusions. In the special important case of linear and quadratic programming problems, salient dynamical features of G-NPC, namely the presence of sliding modes , trajectory convergence in finite time, and the ability to compute the exact optimal solution of the problem being modeled, are uncovered and explained in the developed analytical framework.
235 citations
TL;DR: In this paper, a mixed-integer nonlinear programming (MINLP) technique is used to solve the problem of selecting compounds with optimum value of an appropriate performance index, subject to material balances, process and design limitations and feasibility of molecular structures.
235 citations
TL;DR: Comparing the properties of solutions generated by simultaneous approaches to those of classical variational methods, for a variety of problem classes, shows why simultaneous strategies are especially beneficial for dynamic systems with unstable modes, with path constraints and for large-scale, structured problems.
234 citations
TL;DR: In this paper, a retailer decides its level of involvement in the futures market and in the pool as well as the selling price offered to its potential clients with the goal of maximizing the expected profit at a given risk level.
Abstract: This paper presents a bilevel programming approach to solve the medium-term decision-making problem faced by a power retailer. A retailer decides its level of involvement in the futures market and in the pool as well as the selling price offered to its potential clients with the goal of maximizing the expected profit at a given risk level. Uncertainty on future pool prices, client demands, and rival-retailer prices is accounted for via stochastic programming. Unlike in previous approaches, client response to retail price and competition among rival retailers are both explicitly considered in the proposed bilevel model. The resulting nonlinear bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear programming problem by replacing the lower-level optimization by its Karush-Kuhn-Tucker optimality conditions and converting a number of nonlinearities to linear equivalents using some well-known integer algebra results. A realistic case study is solved to illustrate the efficient performance of the proposed methodology.
233 citations
TL;DR: The key feature of the proposed approach is that the on-line optimization problem is solved off-line via parametric programming techniques, and only simple function evaluations are required, to obtain the optimal inputs to the plant for the current state of the plant.
233 citations