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

Ting-Jang Shiu () and Soon-Yi Wu ()

Computational Optimization and Applications, 2012, vol. 53, issue 1, 113 pages

Abstract: 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 αBB 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. Copyright Springer Science+Business Media, LLC 2012

Keywords: Nonlinear semi-infinite programming; Convexification approximation; Cutting plane method; Control design problem (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-011-9452-9

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