THE EXACT FEASIBILITY OF RANDOMIZED SOLUTIONS OF UNCERTAIN CONVEX PROGRAMS

作     者：Campi, M. C. Garatti, S. 

作者机构：Univ Brescia Dipartimento Elettron Automaz I-25123 Brescia Italy Politecn Milan Dipartimento Elettron & Informaz I-20133 Milan Italy 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 (工业与应用数学会最优化杂志)

年 卷 期：2008年第19卷第3期

页      面：1211-1230页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：uncertain optimization randomized methods convex optimization semi-infinite programming robust optimization chance-constrained 

摘      要：Many optimization problems are naturally delivered in an uncertain framework, and one would like to exercise prudence against the uncertainty elements present in the problem. In previous contributions, it has been shown that solutions to uncertain convex programs that bear a high probability to satisfy uncertain constraints can be obtained at low computational cost through constraint randomization. In this paper, we establish new feasibility results for randomized algorithms. Specifically, the exact feasibility for the class of the so-called fully-supported problems is obtained. It turns out that all fully-supported problems share the same feasibility properties, revealing a deep kinship among problems of this class. It is further proven that the feasibility of the randomized solutions for all other convex programs can be bounded based on the feasibility for the prototype class of fully-supported problems. The feasibility result of this paper outperforms previous bounds and is not improvable because it is exact for fully-supported problems.