Constrained global optimization: algorithms and applications
Constrained global optimization: algorithms and applications
Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
Experiments in quadratic 0-1 programming
Mathematical Programming: Series A and B
Construction of test problems in quadratic bivalent programming
ACM Transactions on Mathematical Software (TOMS)
On approximation algorithms for concave quadratic programming
Recent advances in global optimization
A branch and bound algorithm for the maximum clique problem
Computers and Operations Research
On affine scaling algorithms for nonconvex quadratic programming
Mathematical Programming: Series A and B
Convex relaxations of (0, 1)-quadratric programming
Mathematics of Operations Research
Newton-KKT interior-point methods for indefinite quadratic programming
Computational Optimization and Applications
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In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace.