SDP vs. LP relaxations for the moment approach in some performance evaluation problems
نویسندگان
چکیده
Given a Markov process we are interested in the numerical computation of the moments of the exit time from a bounded domain. We use a moment approach which, together with appropriate semidefinite positivity moment conditions, yields a sequence of semidefinite programs (or SDP relaxations), depending on the number of moments considered, that provide a sequence of nonincreasing (resp. nondecreasing) upper (resp. lower) bounds. The results are compared to the linear Hausdorff moment conditions approach considered for the LP relaxations in [1]. The SDP relaxations are shown to be more general and more precise than the LP relaxations.
منابع مشابه
The Power of Semidefinite Programming Relaxations for MAX-SAT
Recently, Linear Programming (LP)-based relaxations have been shown promising in boosting the performance of exact MAX-SAT solvers. We compare Semidefinite Programming (SDP) based relaxations with LP relaxations for MAX2SAT. We will show how SDP relaxations are surprisingly powerful, providing much tighter bounds than LP relaxations, across different constrainedness regions. SDP relaxations can...
متن کاملCones of Matrices and Successive Convex Relaxations of Nonconvex Sets
Let F be a compact subset of the n-dimensional Euclidean space Rn represented by (finitely or infinitely many) quadratic inequalities. We propose two methods, one based on successive semidefinite programming (SDP) relaxations and the other on successive linear programming (LP) relaxations. Each of our methods generates a sequence of compact convex subsets Ck (k = 1, 2, . . . ) of Rn such that (...
متن کاملLift & Project Systems Performing on the Partial Vertex Cover Polytope
We study integrality gap (IG) lower bounds on strong LP and SDP relaxations derived by the SheraliAdams (SA), Lovász-Schrijver-SDP (LS+), and Sherali-Adams-SDP (SA+) lift-and-project (L&P) systems for the t-Partial-Vertex-Cover (t-PVC) problem, a variation of the classic Vertex-Cover problem in which only t edges need to be covered. t-PVC admits a 2-approximation using various algorithmic techn...
متن کاملSemidefinite Programming vs. LP Relaxations for Polynomial Programming
We consider the global minimization of a multivariate polynomial on a semi-algebraic set defined with polynomial inequalities. We then compare two hierarchies of relaxations, namely, LP relaxations based on products of the original constraints, in the spirit of the RLT procedure of Sherali and Adams (1990), and recent semidefinite programming (SDP) relaxations introduced by the author. The comp...
متن کاملExact SDP Relaxations with Truncated Moment Matrix for Binary Polynomial Optimization Problems
For binary polynomial optimization problems (POPs) of degree d with n variables, we prove that the ⌈(n+ d− 1)/2⌉th semidefinite (SDP) relaxation in Lasserre’s hierarchy of the SDP relaxations provides the exact optimal value. If binary POPs involve only even-degree monomials, we show that it can be further reduced to ⌈(n + d − 2)/2⌉. This bound on the relaxation order coincides with the conject...
متن کامل