Optimization of a convex program with a polynomial perturbation

Authors:
Ravi Kannan;Luis Rademacher
Affiliations:
Microsoft Research Bangalore, India;College of Computing, Georgia Institute of Technology, United States
Venue:
Operations Research Letters
Year:
2009

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Abstract

We consider the problem of minimizing a convex function plus a polynomial p over a convex body K. We give an algorithm that outputs a solution x whose value is within @erange"K(p) of the optimum value, where range"K(p)=sup"x"@?"Kp(x)-inf"x"@?"Kp(x). When p depends only on a constant number of variables, the algorithm runs in time polynomial in 1/@e, the degree of p, the time to round K and the time to solve the convex program that results by setting p=0.