On the Central Paths in Symmetric Cone Programming
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- 作者：Héctor Ramírez ; David Sossa
- 关键词：Symmetric cone programming ; Central paths ; Barrier functions ; Recession functions ; Euclidean Jordan algebra
- 刊名：Journal of Optimization Theory and Applications
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：172
- 期：2
- 页码：649-668
- 全文大小：
- 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
- 出版者：Springer US
- ISSN：1573-2878
- 卷排序：172
文摘
This paper is devoted to the study of optimal solutions of symmetric cone programs by means of the asymptotic behavior of central paths with respect to a broad class of barrier functions. This class is, for instance, larger than that typically found in the literature for semidefinite positive programming. In this general framework, we prove the existence and the convergence of primal, dual and primal–dual central paths. We are then able to establish concrete characterizations of the limit points of these central paths for specific subclasses. Indeed, for the class of barrier functions defined at the origin, we prove that the limit point of a primal central path minimizes the corresponding barrier function over the solution set of the studied symmetric cone program. In addition, we show that the limit points of the primal and dual central paths lie in the relative interior of the primal and dual solution sets for the case of the logarithm and modified logarithm barriers.