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We demonstrate that if A 1 ; :::; A m are symmetric positive semideenite n n matrices with positive deenite sum and A is an arbitrary symmetric n n matrix, then the quality of the semideenite relaxation (P) is not worse than 1 2 ln(2m 2). It is shown that this bound is sharp in order, as far as the dependence on m is concerned, and that a feasible solution(More)
Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case.(More)
In this survey we review the many faces of the S-lemma, a result about the cor-rectness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry and linear algebra as well. These were active research areas, but as there was little(More)
Sensitivity analysis is one of the most interesting and preoccupying areas in optimization. Many attempts are made to investigate the problem's behavior when the input data changes. Usually variation occurs in the right hand side of the constraints and/or the objective function coefficients. Degeneracy of optimal solutions causes considerable difficulties(More)
A standard quadratic problem consists of nding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semideenite programming relaxation is strengthened by replacing the cone of positive semideenite matrices by the cone of completely positive matrices (the positive semideenite matrices which allow a factorization F F T(More)
No part of this Journal may be reproduced in any form, by print, photoprint, microolm or any other means without written permis-ii Abstract In this paper we propose a large{step analytic center method for smooth convex programming. The method is a natural implementation of the classical method of centers. It is assumed that the objective and constraint(More)