SYMMETRIC STRONG DUALITY FOR A CLASS OF CONTINUOUS LINEAR PROGRAMS WITH CONSTANT COEFFICIENTS

作     者：Shindin, Evgeny Weiss, Gideon 

作者机构：Univ Haifa Dept Stat IL-31905 Har Hakarmel Israel 

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

年 卷 期：2014年第24卷第3期

页      面：1102-1121页

核心收录：

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

基　　金：Israel Science Foundation [711/09  286/13] 

主　　题：continuous linear programming symmetric dual strong duality 

摘      要：We consider continuous linear programs over a continuous finite time horizon T, with linear cost coefficient functions and linear right-hand side functions and a constant coefficient matrix, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the separated continuous linear programming models and their various duals, as formulated in the past by Anderson, by Pullan, and by Weiss. We present simple necessary and sufficient conditions for feasibility. We formulate a symmetric dual and investigate strong duality by considering discrete time approximations. We prove that under a Slater type condition there is no duality gap and there exist optimal solutions which have impulse controls at 0 and T and have piecewise constant densities in (0, T). Moreover, we show that under nondegeneracy assumptions all optimal solutions are of this form, and are uniquely determined over (0, T).