Semi-infinite programming: Theory, methods, and applications

Semi-infinite programming: Theory, methods, and applications

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Article ID: iaor1994729
Country: United States
Volume: 53
Issue: 3
Start Page Number: 380
End Page Number: 419
Publication Date: Sep 1993
Journal: SIAM Math Rev
Authors: ,
Keywords: semi-infinite programming
Abstract:

Starting from a number of motivating and abundant applications in ℝ2, 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 ℝℝ3-5, 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 ℝ6. 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 complementary to the review given by Polak on the nondifferentiable approach. The last, short section briefly reviews some work done on parametric problems.

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