Block-diagonal semidefinite programming hierarchies for 0/1 programming

نویسندگان

  • Nebojsa Gvozdenovic
  • Monique Laurent
  • Frank Vallentin
چکیده

Lovász and Schrijver, and later Lasserre, proposed hierarchies of semidefinite programming relaxations for 0/1 linear programming problems. We revisit these two constructions and propose two new, blockdiagonal hierarchies, which are at least as strong as the Lovász–Schrijver hierarchy, but less costly to compute. We report experimental results for the stable set problem of Paley graphs. © 2008 Elsevier B.V. All rights reserved.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Recurrent Neural Network Model for Solving Linear Semidefinite Programming

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...

متن کامل

CORC Technical Report TR-2001-03 Cuts for mixed 0-1 conic programming

In this we paper we study techniques for generating valid convex constraints for mixed 0-1 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 0-1 linear programs, such as the Gomory cuts, the lift-and-project cuts, and cuts from other hierarchies of tighter relaxations, extend in a straightforward manner to mixed 0-1 conic programs. We also show t...

متن کامل

A Simple Path-following Algorithm for the Feasibility Problem in Semidefinite Programming and for Matrix Scaling over the Semidefinite Cone

Let E be the Hilbert space of symmetric matrices of the form diag(A,M), where A is n× n, and M is an l× l diagonal matrix, and the inner product 〈x, y〉 ≡ Trace(xy). Given x ∈ E, we write x ≥ 0 (x > 0) if it is positive semidefinite (positive definite). Let Q : E → E be a symmetric positive semidefinite linear operator, and μ = min{φ(x) = 0.5Trace(xQx) : ‖x‖ = 1, x ≥ 0}. The feasibility problem ...

متن کامل

Conditioning of semidefinite programs

This paper studies the conditioning of semidefinite programs by analyzing the effect of small perturbations in problem data on the solution. Under the assumptions of strict complementarity and nondegeneracy, an explicit bound on the change in the solution is derived in a primal-dual framework, using tools from the Kantorovič theory. This approach also quantifies the size of permissible perturba...

متن کامل

Exponential lower bounds on fixed-size psd rank and semidefinite extension complexity

There has been a lot of interest recently in proving lower bounds on the size of linear programs needed to represent a given polytope P . In a breakthrough paper Fiorini et al. [FMP12] showed that any linear programming formulation of maximum-cut must have exponential size. A natural question to ask is whether one can prove such strong lower bounds for semidefinite programming formulations. In ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Oper. Res. Lett.

دوره 37  شماره 

صفحات  -

تاریخ انتشار 2009