Barrier methods based on Jordan-Hilbert algebras for stochastic optimization in spin factors

作     者：Alzalg, Baha 

作者机构：Univ Jordan Dept Math Amman 11942 Jordan 

出 版 物：《RAIRO-OPERATIONS RESEARCH》 (RAIRO Oper. Res.)

年 卷 期：2024年第58卷第1期

页      面：1011-1044页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

主　　题：Jordan-Hilbert algebras second-order cone programming programming in abstract spaces stochastic programming interior-point methods stochastic control 

摘      要：Infinite-dimensional stochastic second-order cone programming involves minimizing linear functions over intersections of affine linear manifolds with infinite-dimensional second-order cones. However, even though there is a legitimate necessity to explore these methods in general spaces, there is an absence of infinite-dimensional counterparts for these methods. In this paper, we present decomposition logarithmic-barrier interior-point methods based on unital Jordan-Hilbert algebras for this class of optimization problems in the infinite-dimensional setting. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best-known complexity obtained by such methods for the finite-dimensional setting. We apply our results to an important problem in stochastic control, namely the two-stage stochastic multi-criteria design problem. We show that the corresponding infinite-dimensional system in this case is a matrix differential Ricatti equation plus a finite-dimensional system, and hence, it can be solved efficiently to find the search direction.