Beyond Canonical DC-Optimization: The Single Reverse Polar Problem

作者：Bigi Giancarlo^*; Frangioni Antonio; Zhang Qinghua

来源：Journal of Optimization Theory and Applications, 2012, 155(2): 430-452.

DOI：10.1007/s10957-012-0069-7

• Single reverse polar problems
• Approximate optimality conditions
• Cutting plane algorithms

We propose a novel generalization of the Canonical Difference of Convex problem (CDC), and we study the convergence of outer approximation algorithms for its solution, which use an approximated oracle for checking the global optimality conditions. Although the approximated optimality conditions are similar to those of CDC, this new class of problems is shown to significantly differ from its special case. Indeed, outer approximation approaches for CDC need be substantially modified in order to cope with the more general problem, bringing to new algorithms. We develop a hierarchy of conditions that guarantee global convergence, and we build three different cutting plane algorithms relying on them.

• 出版日期2012-11
• 单位武汉大学