Relaxed cutting plane method with convexification for solving nonlinear semi-infinite programming problems

In this paper, we present an algorithm to solve nonlinear semi-infinite programming (NSIP) problems. To deal with the nonlinear constraint, Floudas and Stein (SIAM J. Optim. 18:1187–1208, 2007 ) suggest an adaptive convexification relaxation to approximate the nonlinear constraint function. The α BB...

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Vydáno v:Computational optimization and applications Ročník 53; číslo 1; s. 91 - 113
Hlavní autoři: Shiu, Ting-Jang, Wu, Soon-Yi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.09.2012
Springer Nature B.V
Témata:
Algorithms
Approximation
Convex and Discrete Geometry
Cutting
Impulse response
Management Science
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Nonlinear programming
Nonlinearity
Operations Research
Operations Research/Decision Theory
Optimization
Optimization algorithms
Production planning
Programming
Statistics
Studies
Nonlinear semi-infinite programming
Control design problem
Convexification approximation
Cutting plane method
ISSN:0926-6003, 1573-2894
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Shrnutí:In this paper, we present an algorithm to solve nonlinear semi-infinite programming (NSIP) problems. To deal with the nonlinear constraint, Floudas and Stein (SIAM J. Optim. 18:1187–1208, 2007 ) suggest an adaptive convexification relaxation to approximate the nonlinear constraint function. The α BB method, used widely in global optimization, is applied to construct the convexification relaxation. We then combine the idea of the cutting plane method with the convexification relaxation to propose a new algorithm to solve NSIP problems. With some given tolerances, our algorithm terminates in a finite number of iterations and obtains an approximate stationary point of the NSIP problems. In addition, some NSIP application examples are implemented by the method proposed in this paper, such as the proportional-integral-derivative controller design problem and the nonlinear finite impulse response filter design problem. Based on our numerical experience, we demonstrate that our algorithm enhances the computational speed for solving NSIP problems.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-011-9452-9