An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems

Tianxiang Liu () and Akiko Takeda ()
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Tianxiang Liu: Tokyo Institute of Technology
Akiko Takeda: The University of Tokyo

Computational Optimization and Applications, 2022, vol. 82, issue 1, No 7, 173 pages

Abstract: Abstract In this paper, we propose a new method for a class of difference-of-convex (DC) optimization problems, whose objective is the sum of a smooth function and a possibly non-prox-friendly DC function. The method sequentially solves subproblems constructed from a quadratic approximation of the smooth function and a linear majorization of the concave part of the DC function. We allow the subproblem to be solved inexactly, and propose a new inexact rule to characterize the inexactness of the approximate solution. For several classical algorithms applied to the subproblem, we derive practical termination criteria so as to obtain solutions satisfying the inexact rule. We also present some convergence results for our method, including the global subsequential convergence and a non-asymptotic complexity analysis. Finally, numerical experiments are conducted to illustrate the efficiency of our method.

Keywords: DC programming; Quadratic approximation; Inexact rule; Non-asymptotic complexity (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-022-00357-z

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