Results 1  10
of
73,121
Trust Regions and Relaxations for the Quadratic Assignment Problem
 IN QUADRATIC ASSIGNMENT AND RELATED PROBLEMS (NEW
, 1993
"... General quadratic matrix minimization problems, with orthogonal constraints, arise in continuous relaxations for the (discrete) quadratic assignment problem (QAP). Currently, bounds for QAP are obtained by treating the quadratic and linear parts of the objective function, of the relaxations, separat ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
General quadratic matrix minimization problems, with orthogonal constraints, arise in continuous relaxations for the (discrete) quadratic assignment problem (QAP). Currently, bounds for QAP are obtained by treating the quadratic and linear parts of the objective function, of the relaxations
Strong Duality for a TrustRegion Type Relaxation of the Quadratic Assignment Problem
, 1998
"... Lagrangian duality underlies many efficient algorithms for convex minimization problems. A key ingredient is strong duality. Lagrangian relaxation also provides lower bounds for nonconvex problems, where the quality of the lower bound depends on the duality gap. Quadratically constrained quadratic p ..."
Abstract

Cited by 15 (9 self)
 Add to MetaCart
for the two trust region subproblem. Surprisingly, there are classes of more complex, nonconvex QQPs where strong duality holds. One example is the special case of orthogonality constraints, which arise naturally in relaxations for the quadratic assignment problem (QAP). In this paper we show that strong
On Lagrangian relaxation of quadratic matrix constraints
 SIAM J. MATRIX ANAL. APPL
, 2000
"... Quadratically constrained quadratic programs (QQPs) play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Lagrangian relaxations often provide good approximate solutions to these hard problems. Such relaxations are equivalent ..."
Abstract

Cited by 50 (17 self)
 Add to MetaCart
zero duality gap. This result has natural applications to quadratic assignment and graph partitioning problems, as well as the problem of minimizing the weighted sum of the largest eigenvalues of a matrix. We also show that the technique of relaxing quadratic matrix constraints can be used to obtain a
Semidefinite Programming Approaches To The Quadratic Assignment Problem
, 2000
"... The Quadratic Assignment Problem, QAP, is arguably the hardest of the NPhard problems. One of the main reasons is that it is very difficult to get good quality bounds for branch and bound algorithms. We show that many of the bounds that have appeared in the literature can be ranked and put into a u ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
The Quadratic Assignment Problem, QAP, is arguably the hardest of the NPhard problems. One of the main reasons is that it is very difficult to get good quality bounds for branch and bound algorithms. We show that many of the bounds that have appeared in the literature can be ranked and put into a
A recipe for semidefinite relaxation for 01 quadratic programming
 JOURNAL OF GLOBAL OPTIMIZATION
, 1995
"... We review various relaxations of (0,1)quadratic programming problems. These include semidefinite programs, parametric trust region problems and concave quadratic maximization. All relaxations that we consider lead to efficiently solvable problems. The main contributions of the paper are the followi ..."
Abstract

Cited by 56 (7 self)
 Add to MetaCart
We review various relaxations of (0,1)quadratic programming problems. These include semidefinite programs, parametric trust region problems and concave quadratic maximization. All relaxations that we consider lead to efficiently solvable problems. The main contributions of the paper
On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming
"... presented to the University of Waterloo ..."
A Matrixlifting Semidefinite Relaxation for the Quadratic Assignment Problem
, 2006
"... The quadratic assignment problem (QAP) is arguably one of the hardest of the NPhard discrete optimization problems. Problems of dimension greater than 20 are considered to be large scale. Current successful solution techniques depend on branch and bound methods. However, it is di#cult to get strong ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
The quadratic assignment problem (QAP) is arguably one of the hardest of the NPhard discrete optimization problems. Problems of dimension greater than 20 are considered to be large scale. Current successful solution techniques depend on branch and bound methods. However, it is di#cult to get
Semidefinite Relaxations of the Quadratic Assignment Problem in a Lagrangian Framework
"... Abstract. In this paper, we consider partial Lagrangian relaxations of continuous quadratic formulations of the Quadratic Assignment Problem (QAP) where the assignment constraints are not relaxed. These relaxations are a theoretical limit for semidefinite relaxations of the QAP using any linearized ..."
Abstract
 Add to MetaCart
Abstract. In this paper, we consider partial Lagrangian relaxations of continuous quadratic formulations of the Quadratic Assignment Problem (QAP) where the assignment constraints are not relaxed. These relaxations are a theoretical limit for semidefinite relaxations of the QAP using any linearized
New Results on Quadratic Minimization
, 2001
"... In this paper we present several new results on minimizing an indefinite quadratic function under quadratic/linear constraints. The emphasis is placed on the case where the constraints are two quadratic inequalities. This formulation is known as the extended trust region subproblem and the computati ..."
Abstract

Cited by 62 (8 self)
 Add to MetaCart
of quadratic optimization. For the extended trust region subproblem itself, we introduce a parameterized problem and prove the existence of a trajectory which will lead to an optimal solution. Combining with a result obtained in the first part of the paper, we propose a polynomialtime solution procedure
Results 1  10
of
73,121