Gap inequalities for non-convex mixed-integer quadratic programs

نویسندگان

  • Laura Galli
  • Konstantinos Kaparis
  • Adam N. Letchford
چکیده

Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general nonconvex mixed-integer quadratic programs. These inequalities dominate some inequalities arising from a natural semidefinite relaxation.

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 note on representations of linear inequalities in non-convex mixed-integer quadratic programs

In the literature on the quadratic 0-1 knapsack problem, several alternative ways have been given to represent the knapsack constraint in the quadratic space. We extend this work by constructing analogous representations for arbitrary linear inequalities for arbitrary nonconvex mixed-integer quadratic programs with bounded variables.

متن کامل

On Valid Inequalities for Quadratic Programming with Continuous Variables and Binary Indicators

In this paper we study valid inequalities for a set that involves a continuous vector variable x ∈ [0, 1], its associated quadratic form xx , and binary indicators on whether or not x > 0. This structure appears when deriving strong relaxations for mixed integer quadratic programs (MIQPs). Valid inequalities for this set can be obtained by lifting inequalities for a related set without binary v...

متن کامل

On the separation of split inequalities for non-convex quadratic integer programming

We investigate the computational potential of split inequalities for non-convex quadratic integer programming, first introduced by Letchford [11] and further examined by Burer and Letchford [8]. These inequalities can be separated by solving convex quadratic integer minimization problems. For small instances with box-constraints, we show that the resulting dual bounds are very tight; they can c...

متن کامل

Unbounded convex sets for non-convex mixed-integer quadratic programming

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some o...

متن کامل

Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-a...

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 39  شماره 

صفحات  -

تاریخ انتشار 2011