The nature of statistical learning theory
The nature of statistical learning theory
Coupled optimization in protein docking
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Convex Quadratic Approximation
Computational Optimization and Applications
Global Minimization via Piecewise-Linear Underestimation
Journal of Global Optimization
Optimization Methods & Software
An aggregate deformation homotopy method for min-max-min problems with max-min constraints
Computational Optimization and Applications
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Motivated by the fact that important real-life problems, such as the protein docking problem, can be accurately modeled by minimizing a nonconvex piecewise-quadratic function, a nonconvex underestimator is constructed as the minimum of a finite number of strictly convex quadratic functions. The nonconvex underestimator is generated by minimizing a linear function on a reverse convex region and utilizes sample points from a given complex function to be minimized. The global solution of the piecewise-quadratic underestimator is known exactly and gives an approximation to the global minimum of the original function. Successive shrinking of the initial search region to which this procedure is applied leads to fairly accurate estimates, within 0.0060%, of the global minima of synthetic nonconvex functions for which the global minima are known. Furthermore, this process can approximate a nonconvex protein docking function global minimum within four-figure relative accuracy in six refinement steps. This is less than half the number of refinement steps required by previous models such as the convex kernel underestimator (Mangasarian et al., Computational Optimization and Applications, to appear) and produces higher accuracy here.