An inverse problem in convex optimization

Dissertant

Masarwah, Nuha

Thesis advisor

al-Uqayli, Marwan

Comitee Members

Musa, Abd al-Rahim
Ilayyan, Ala al-Din

University

Birzeit University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (West Bank)

Degree

Master

Degree Date

2016

English 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.

Main Subjects

Mathematics

No. of Pages

61

Table of Contents

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• MLA
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Language

English

Data Type

Arab Theses

Record ID

BIM-728296