Constrained Extremum Problems and Image Space Analysis—Part III: Generalized Systems

Shengjie Li (), Yangdong Xu (), Manxue You () and Shengkun Zhu ()
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Shengjie Li: Chongqing University
Yangdong Xu: Chongqing University of Posts and Telecommunications
Manxue You: Chongqing University
Shengkun Zhu: Southwestern University of Finance and Economics

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 5, 660-678

Abstract: Abstract In Part I, sufficient and necessary optimality conditions and the image regularity conditions of constrained scalar and vector extremum problems are reviewed for Image Space Analysis. Part II presents the main feature of the duality and penalization of constrained scalar and vector extremum problems by virtue of Image Space Analysis. In the light, as said in Part I and Part II, to describe the state of Image Space Analysis for constrained optimization, and to stress that it allows us to unify and generalize the several topics of Optimization, in this Part III, we continue to give an exhaustive literature review on separation functions, gap functions and error bounds for generalized systems. Part III also throws light on some research gaps and concludes with the scope of future research in this area.

Keywords: Image space analysis; Generalized system; Separation function; Gap function; Error bound; 49K05; 90C29 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-018-1249-x

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