A branch and bound algorithm for the maximum clique problem
Computers and Operations Research
A decomposition method for quadratic zero-one programming
Management Science
Convex relaxations of (0, 1)-quadratric programming
Mathematics of Operations Research
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
A scatter search approach to unconstrained quadratic binary programs
New ideas in optimization
Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs
SIAM Journal on Optimization
IEEE Computational Science & Engineering
Discrete Applied Mathematics
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
An algorithm for nonlinear optimization problems with binary variables
Computational Optimization and Applications
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In this paper, we propose a new continuous approach for the unconstrained binary quadratic programming (BQP) problems based on the Fischer-Burmeister NCP function. Unlike existing relaxation methods, the approach reformulates a BQP problem as an equivalent continuous optimization problem, and then seeks its global minimizer via a global continuation algorithm which is developed by a sequence of unconstrained minimization for a global smoothing function. This smoothing function is shown to be strictly convex in the whole domain or in a subset of its domain if the involved barrier or penalty parameter is set to be sufficiently large, and consequently a global optimal solution can be expected. Numerical results are reported for 0-1 quadratic programming problems from the OR-Library, and the optimal values generated are made comparisons with those given by the well-known SBB and BARON solvers. The comparison results indicate that the continuous approach is extremely promising by the quality of the optimal values generated and the computational work involved, if the initial barrier parameter is chosen appropriately.