In this paper, our central notions of analysis are convexity and betweenness. These concepts are given from the viewpoint of conceptual spaces and are specified in relation to the coordinates of a polar system. We introduce and study a problem that seeks to optimize a polar convex objective subject to polar convex constraints, which we refer to as the polar convex programming problem. We utilize a geometric methodology to solve the two-dimensional version of this optimization problem. Our interpretation of the approach is inspired by the classical graphical method for linear optimization problems. To the best of our knowledge, this family of optimization problems has not yet been addressed or even raised by researchers.
Digital Object Identifier (DOI)
Benakkouche, Lilia; Whitman, Blake; and Alzalg, Baha
"Polar Convex Programming: A New Paradigm for Nonlinear Optimization,"
Applied Mathematics & Information Sciences: Vol. 17:
3, Article 15.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss3/15