A Unified Approach for Constrained Extremum Problems: Image Space Analysis

J. Li (), S. Q. Feng () and ZhongXiang Zhang
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J. Li: China West Normal University
S. Q. Feng: China West Normal University

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 1, No 4, 69-92

Abstract: Abstract In this paper, by exploiting the image space analysis we investigate a class of constrained extremum problems, the constraining function of which is set-valued. We show that a (regular) linear separation in the image space is equivalent to the existence of saddle points of Lagrangian and generalized Lagrangian functions and we also give Lagrangian type optimality conditions for the class of constrained extremum problems under suitable generalized convexity and compactness assumptions. Moreover, we consider an exact penalty problem for the class of constrained extremum problems and prove that it is equivalent to the existence of a regular linear separation under suitable generalized convexity and compactness assumptions.

Keywords: Image space analysis; Linear separation; Saddle points; Penalty methods; Constrained extremum problems (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s10957-013-0276-x

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