2015/03/31 by Mahmood Mehdiloozad, Kaoru Tone, Mehdiloozad, Mahmood +5
Decision Sciences · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Vehicle Routing Optimization Methods
paper · pdf · doi:10.48550/arxiv.1503.09014
openalex publication_date 2015/03/31 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motzkin (1936) made a transition from the polyhedron to a polyhedral cone. Based on his excellent idea, we represent a set by a characteristic cone. By using this representation, we then reach four main results: (i) expressing a closed convex set containing no line as the direct sum of the convex hull of its extreme points and conical hull of its extreme directions, (ii) establishing a convex programming (CP) based framework for determining a maximal element-an element with the maximum number of positive components-of a convex set, (iii) developing a linear programming problem for finding a relative interior point of a polyhedron, and (iv) proposing two procedures for the identification of a strictly complementary solution in linear programming.