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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
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Journal ArticleDOI
TL;DR: A deterministic method is proposed for the global optimization of mathematical programs that involve the sum of linear fractional and/or bilinear terms and it is shown that additional estimators can be obtained through projections of the feasible region.
Abstract: In this paper a deterministic method is proposed for the global optimization of mathematical programs that involve the sum of linear fractional and/or bilinear terms. Linear and nonlinear convex estimator functions are developed for the linear fractional and bilinear terms. Conditions under which these functions are nonredundant are established. It is shown that additional estimators can be obtained through projections of the feasible region that can also be incorporated in a convex nonlinear underestimator problem for predicting lower bounds for the global optimum. The proposed algorithm consists of a spatial branch and bound search for which several branching rules are discussed. Illustrative examples and computational results are presented to demonstrate the efficiency of the proposed algorithm.

149 citations

Proceedings ArticleDOI
05 Nov 2000
TL;DR: A new class of fast and highly scalable placement algorithms that directly handle complex constraints and achieve total wirelengths comparable to the state of the art are designed and implemented.
Abstract: We have designed and implemented a new class of fast and highly scalable placement algorithms that directly handle complex constraints and achieve total wirelengths comparable to the state of the art. Our approach exploits recent advances in (i) multilevel methods for hierarchical computation, (ii) interior-point methods for nonconvex nonlinear programming, and (iii) the Fast Multipole Method for the order N evaluation of sums over the N (N - 1)/2 pairwise interactions of N components. Significant adaptation of these methods for the placement problem is required, and we have therefore developed a set of customized discrete algorithms for clustering, declustering, slot assignment, and local refinement with which the continuous algorithms are naturally combined. Preliminary test runs on benchmark circuits with up to 184,000 cells produce total wirelengths within approximately 5-10% of those of GORDIAN-L [1] in less than one tenth the run time. Such an ultra-fast placement engine is badly needed for timing convergence of the synthesis and layout phases of integrated circuit design.

149 citations

Journal ArticleDOI
TL;DR: In this paper, a GA-Benders' decomposition (GA-BD) method is proposed for solving the power generation expansion planning problem with emission control, and an application of the proposed GA-BD method is discussed and concluded.
Abstract: The power generation expansion planning (PGEP) problem is a large-scale mixed integer nonlinear programming (MINLP) problem cited as one of the most complex optimization problems. In this paper, an application of a new efficient methodology for solving the power generation expansion planning problem is presented. A comprehensive planning production simulation model is introduced toward formulating into an MINLP model. The model evaluates the most economical investment planning for additional thermal power generating units of the optimal mix for long-term power generation expansion planning with emission controls, regarding to the incorporated environmental costs, subject to the integrated requirements of power demands, power capacities, loss of load probability (LOLP) levels, locations, and environmental limitations for emission controls. A GA-heuristic-based method called GA-Benders' decomposition (GA-BD) is proposed for solving this complex problem. Finally, an application of the proposed GA-BD method is discussed and concluded.

148 citations

Journal ArticleDOI
TL;DR: Applications of the path search include damping Robinson-Newton's method for nonsmooth normal equations corresponding to nonlinear complementarity problems and variational inequalities, hence damping both Wilson's method (sequential quadratic programming) for nonlinear programming and Josephy-Newtons method for generalized equations.
Abstract: A natural damping of Newton's method for nonsmooth equations is presented. This damping, via the path search instead of the traditional line search, enlarges the domain of convergence of Newton's method and therefore is said to be globally convergent. Convergence behavior is like that of line search damped Newton's method for smooth equations, including Q-quadratic convergence rates under appropriate conditions. Applications of the path search include damping Robinson-Newton's method for nonsmooth normal equations corresponding to nonlinear complementarity problems and variational inequalities, hence damping both Wilson's method (sequential quadratic programming) for nonlinear programming and Josephy-Newton's method for generalized equations. Computational examples from nonlinear programming are given.

148 citations

Journal ArticleDOI
TL;DR: This work considers the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bileVEL programs involving linear approximations of the upper-level objective and all constraint-defining functions.
Abstract: We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments tend to confirm the promising behavior of the method.

148 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023113
2022259
2021615
2020650
2019640
2018630