An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Constrained global optimization: algorithms and applications
Constrained global optimization: algorithms and applications
A continuous approach to nonlinear integer programming
Applied Mathematics and Computation
Construction of test problems in quadratic bivalent programming
ACM Transactions on Mathematical Software (TOMS)
Newton methods for large-scale linear equality-constrained minimization
SIAM Journal on Matrix Analysis and Applications
Computing modified Newton directions using a partial Cholesky factorization
SIAM Journal on Scientific Computing
Global Continuation for Distance Geometry Problems
SIAM Journal on Optimization
Infeasibility and negative curvature in optimization
Infeasibility and negative curvature in optimization
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
A global continuation algorithm for solving binary quadratic programming problems
Computational Optimization and Applications
Computational Optimization and Applications
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One of the challenging optimization problems is determining the minimizer of a nonlinear programming problem that has binary variables. A vexing difficulty is the rate the work to solve such problems increases as the number of discrete variables increases. Any such problem with bounded discrete variables, especially binary variables, may be transformed to that of finding a global optimum of a problem in continuous variables. However, the transformed problems usually have astronomically large numbers of local minimizers, making them harder to solve than typical global optimization problems. Despite this apparent disadvantage, we show that the approach is not futile if we use smoothing techniques. The method we advocate first convexifies the problem and then solves a sequence of subproblems, whose solutions form a trajectory that leads to the solution. To illustrate how well the algorithm performs we show the computational results of applying it to problems taken from the literature and new test problems with known optimal solutions.