
Journal of Convex Analysis 25 (2018), No. 3, 717736 Copyright Heldermann Verlag 2018 Inverse Problem in Convex Optimization with Linear Homogeneous Constraints Noha Masarwah Dept. of Mathematics, Birzeit University, P. O. Box 14, Birzeit, Palestine nohamasarwah@gmail.com Marwan Aloqeili Dept. of Mathematics, Birzeit University, P. O. Box 14, Birzeit, Palestine maloqeili@birzeit.edu We characterize solutions of maximization problems under linear constraints that are positively homogeneous of degree one. Necessary and sufficient conditions are given for functions to arise as solutions of such kind of problems. At the same time, we consider the integration problem of homogeneous differential forms in order to solve the inverse problem. Keywords: Inverse problem, multiconstraint maximization, value function, homogeneous differential forms, integrability. MSC: 90C45, 49N45 [ Fulltextpdf (140 KB)] for subscribers only. 