A simplex-type algorithm for continuous linear programs with constant coefficients

• 成果类型: Article
• 署名作者: Shindin, Evgeny; Weiss, Gideon
• 署名单位: International Business Machines (IBM); IBM ISRAEL; University of Haifa
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1353-6
• 发表日期: 2020
• 页码: 157-201
• 关键词: equilibrium points; duality theorem

摘要

We consider continuous linear programs over a continuous finite time horizon T, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions. Specifically, 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. In previous papers we formulated a symmetric dual and have shown strong duality. We also have presented a detailed description of optimal solutions and have defined a combinatorial analogue to basic solutions of standard LP. In this paper we present an algorithm which solves this class of problems in a finite bounded number of steps, using an analogue of the simplex method, in the space of measures.