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OL
2010
104views more  OL 2010»
13 years 3 months ago
On representations of the feasible set in convex optimization
We consider the convex optimization problem minx{f(x) : gj(x) ≤ 0, j = 1, . . . , m} where f is convex, the feasible set K is convex and Slater’s condition holds, but the funct...
Jean B. Lasserre
FOCM
2010
97views more  FOCM 2010»
13 years 3 months ago
Self-Concordant Barriers for Convex Approximations of Structured Convex Sets
We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the ap...
Levent Tunçel, Arkadi Nemirovski
SIAMJO
2000
88views more  SIAMJO 2000»
13 years 4 months ago
A Feasible BFGS Interior Point Algorithm for Solving Convex Minimization Problems
Abstract. We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generat...
Paul Armand, Jean Charles Gilbert, Sophie Jan-J&ea...
CDC
2008
IEEE
291views Control Systems» more  CDC 2008»
13 years 6 months ago
Structured semidefinite representation of some convex sets
Linear matrix Inequalities (LMIs) have had a major impact on control but formulating a problem as an LMI is an art. Recently there is the beginnings of a theory of which problems ...
J. William Helton, Jiawang Nie
CORR
2004
Springer
103views Education» more  CORR 2004»
13 years 4 months ago
Online convex optimization in the bandit setting: gradient descent without a gradient
We study a general online convex optimization problem. We have a convex set S and an unknown sequence of cost functions c1, c2, . . . , and in each period, we choose a feasible po...
Abraham Flaxman, Adam Tauman Kalai, H. Brendan McM...