We consider the computational complexity of optimizing various classes of continuous functions over a simplex, hypercube or sphere.These relatively simple optimization problems have many applications.We review known approximation results as well as negative (inapproximability) results from the recent literature.computational complexity;global optimization;linear and semidefinite programming;approximation algorithms

Klerk, E. de

English

Research Papers in Economics

Approximation algorithms for concave quadratic programming,

astad: Clique is hard to approximate within jV 1¡j,

astad: Some optimal inapproximability results,

Convexity of quadratic transformations and its use in control and optimization.

From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex,

Global optimization of homogeneous polynomials on the simplex and on the sphere,

Improved approximation algorithms for maximum cut and satis¯ability problems using semide¯nite programming,

Improved bounds for the crossing numbers of Km;n and Kn.

Interior point polynomial algorithms in convex programming,

Klerk: Solving standard quadratic optimization problems via linear, semide¯nite and copositive programming,

Maxima for graphs and a new proof of a theorem of T¶ uran,

On the complexity of optimization over the standard simplex,

Parrilo: A PTAS for the minimization of polynomials of ¯xed degree over the simplex, Theoretical Computer Science,

Regularity versus degeneracy in dynamics, games, and optimization: a uni¯ed approach to di®erent aspects,

Semide¯nite programming relaxations of nonconvex quadratic optimization,

Semide¯nite relaxation and nonconvex quadratic optimization,

Structure preserving reductions among convex optimization problems,

The complexity of approximating a nonlinear program,

The Complexity of Optimizing over a Simplex, Hypercube or Sphere: A Short Survey

The Complexity of Optimizing over a Simplex, Hypercube or Sphere: A Short Survey

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics