Derandomizing Approximation Algorithms Based on Semidefinite Programming

On the Optimality of Some Semidefinite Programming-Based Approximation Algorithms under the Unique Games Conjecture

A path-following infeasible interior-point algorithm for semidefinite programming

We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT...

Semidefinite Approximations for Global Unconstrained Polynomial Optimization

We consider the problem of minimizing a polynomial function on R, known to be hard even for degree 4 polynomials. Therefore approximation algorithms are of interest. Lasserre [15] and Parrilo [23] have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations. We propose here a method for computing tight upper ...

Advanced Algorithm Design: Semidefinite Programming (SDP)

In the last few lectures, we considered constant-factor approximation algorithms that relied on linear programming and greedy algorithms. In this lecture, we will analyze algorithms that use a more powerful mathematical programming technique called semidefinite programming. We will illustrate the power of semidefinite programming by looking at the maximum cut problem. However, SDPs are useful f...

Interior Point and Semidefinite Approaches in Combinatorial Optimization

Conic programming, especially semidefinite programming (SDP), has been regarded as linear programming for the 21st century. This tremendous excitement was spurred in part by a variety of applications of SDP in integer programming (IP) and combinatorial optimization, and the development of efficient primal-dual interior-point methods (IPMs) and various first order approaches for the solution of ...