Smoothing Partially Exact Penalty Function of Biconvex Programming

Rui Shen (), Zhiqing Meng and Min Jiang ()
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Rui Shen: School of Economics, Zhejiang University of Technology, Hangzhou 310023, P. R. China
Zhiqing Meng: School of Management, Zhejiang University of Technology, Hangzhou 310023, P. R. China
Min Jiang: School of Management, Zhejiang University of Technology, Hangzhou 310023, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 04, 1-27

Abstract: In this paper, a smoothing partial exact penalty function of biconvex programming is studied. First, concepts of partial KKT point, partial optimum point, partial KKT condition, partial Slater constraint qualification and partial exactness are defined for biconvex programming. It is proved that the partial KKT point is equal to the partial optimum point under the condition of partial Slater constraint qualification and the penalty function of biconvex programming is partially exact if partial KKT condition holds. We prove the error bounds properties between smoothing penalty function and penalty function of biconvex programming when the partial KKT condition holds, as well as the error bounds between objective value of a partial optimum point of smoothing penalty function problem and its 𝜖-feasible solution. So, a partial optimum point of the smoothing penalty function optimization problem is an approximately partial optimum point of biconvex programming. Second, based on the smoothing penalty function, two algorithms are presented for finding a partial optimum or approximate 𝜖-feasible solution to an inequality constrained biconvex optimization and their convergence is proved under some conditions. Finally, numerical experiments show that a satisfactory approximate solution can be obtained by the proposed algorithm.

Keywords: Biconvex programming; partial optimum; smoothing partial exact penalty function; partial exactness; KKT condition (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920400187

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