2014/03/10 by Evgeny Shindin, Shindin, Evgeny, Gideon Weiss +1
Business, Management and Accounting · Decision Sciences · Engineering · Mathematics · #34H99 #49N15 #65K99 #90C48 #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Risk and Portfolio Optimization #Scheduling and Optimization Algorithms #Supply Chain and Inventory Management #math.OC #msc:34H99 #msc:49N15 #msc:65K99 #msc:90C48
paper · pdf · doi:10.48550/arxiv.1403.2186
openalex publication_date 2014/03/10 · arxiv created 2014/11/29 · arxiv updated 2014/12/02 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We consider Continuous Linear Programs over a continuous finite time horizon T, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. 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 a recent paper we have shown that under a Slater type condition, these problems possess optimal strongly dual solutions. In this paper we give a detailed description of optimal solutions and define a combinatorial analog to basic solutions of standard LP. We also show that feasibility implies existence of strongly dual optimal solutions without requiring the Slater condition. We present several examples to illustrate the richness and complexity of these solutions.