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: This paper treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent (SQP-type) methods.
Abstract: Starting from a number of motivating and abundant applications in §2, including control of robots, eigenvalue computations, mechanical stress of materials, and statistical design, the authors describe a class of optimization problems which are referred to as semi-infinite, because their constraints bound functions of a finite number of variables on a whole region. In §§3–5, first- and second-order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints. Another main effort for achieving simplification is through duality in §6. There, algebraic properties of finite linear programming are brought to bear on duality theory in semi-infinite programming. Section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent (SQP-type) methods. Taking this differentiable point of view, this paper can be considered to be complementar...
974 citations
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TL;DR: A nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form that replaces the symmetric, positive semideFinite variable X with a rectangular variable R according to the factorization X=RRT.
Abstract: In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according to the factorization X=RR
T
. The rank of the factorization, i.e., the number of columns of R, is chosen minimally so as to enhance computational speed while maintaining equivalence with the SDP. Fundamental results concerning the convergence of the algorithm are derived, and encouraging computational results on some large-scale test problems are also presented.
967 citations
01 Jan 2016
TL;DR: The linear and nonlinear programming is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
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943 citations
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TL;DR: The development of a computer model GANET is described that involves the application of an area of evolutionary computing, better known as genetic algorithms, to the problem of least-cost design of water distribution networks, an efficient search method for nonlinear optimization problems.
Abstract: This paper describes the development of a computer model GANET that involves the application of an area of evolutionary computing, better known as genetic algorithms, to the problem of least-cost design of water distribution networks. Genetic algorithms represent an efficient search method for nonlinear optimization problems; this method is gaining acceptance among water resources managers/planners. These algorithms share the favorable attributes of Monte Carlo techniques over local optimization methods in that they do not require linearizing assumptions nor the calculation of partial derivatives, and they avoid numerical instabilities associated with matrix inversion. In addition, their sampling is global, rather than local, thus reducing the tendency to become entrapped in local minima and avoiding dependency on a starting point. Genetic algorithms are introduced in their original form followed by different improvements that were found to be necessary for their effective implementation in the optimization of water distribution networks. An example taken from the literature illustrates the approach used for the formulation of the problem. To illustrate the capability of GANET to efficiently identify good designs, three previously published problems have been solved. This led to the discovery of inconsistencies in predictions of network performance caused by different interpretations of the widely adopted Hazen-Williams pipe flow equation in the past studies. As well as being very efficient for network optimization, GANET is also easy to use, having almost the same input requirements as hydraulic simulation models. The only additional data requirements are a few genetic algorithm parameters that take values recommended in the literature. Two network examples, one of a new network design and one of parallel network expansion, illustrate the potential of GANET as a tool for water distribution network planning and management.
939 citations
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TL;DR: In this article, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed, which can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions.
927 citations