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Title: An inverse problem In convex optimization
Authors: Masarwah, Noha
Keywords: Mathematical optimization - Problems, exercises, etc.;Inverse problems (Differential equations) - Numerical solutions;Convex functions
Issue Date: 2016
Abstract: This research aims mainly to solve an inverse problem arising in convex optimization. (P) n max x f(x) ; Ax = C(A), where f is a strictly increasing funnction with respect to each coordinate of the vector x, the Hessian matrix D2 x f is negative definite on the subspace {Dxf} ⊥, f is of class C 2 , A is an m × n matrix of rank m, C : R m×n ++ → R m ++ is homogeneous of degree one and x ∈ R n . We consider a maximization problem under m linear constraints, we characterize the solutions of this kind of problems and give necessary and sufficient conditions for a given function in R n to be the solution of a multi-constraints maximization problem.oblem.
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