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: A systematic procedure to find appropriate values for parameters quickly without much human intervention by using a nonlinear optimization method, the simplex method for nonlinear programming is suggested.
150 citations
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TL;DR: Methods are discussed for the solution of sparse linear equations $Ky = z$, where K is symmetric and indefinite, and direct and iterative methods are both used.
Abstract: Methods are discussed for the solution of sparse linear equations $Ky = z$, where K is symmetric and indefinite. Since exact solutions are not always required, direct and iterative methods are both...
149 citations
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TL;DR: An additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm.
Abstract: Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its 'pure' counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/∼egbirgin/tango/
149 citations
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TL;DR: This work considers an optimal control problem with a nonlinear continuous inequality constraint and proposes an algorithm that computes a sequence of suboptimal controls for the original problem that converges to the minimum cost.
149 citations
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TL;DR: In this article, the authors give necessary optimality conditions for the nonlinear bilevel programming problem and show that the steepest descent direction is obtained by solving a quadratic BLEP.
149 citations