Global Minimization via Piecewise-Linear Underestimation

Authors:
O. L. Mangasarian;J. B. Rosen;M. E. Thompson
Affiliations:
Aff1 Aff2;Department of Computer Science and Engineering, University of California at San Diego, La Jolla, USA 92093;Department of Computer Sciences, University of Wisconsin, Madison, USA 53706
Venue:
Journal of Global Optimization
Year:
2005

Citing 2
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Abstract

Given a function on Rn with many multiple local minima we approximate it from below, via concave minimization, with a piecewise-linear convex function by using sample points from the given function. The piecewise-linear function is then minimized using a single linear program to obtain an approximation to the global minimum of the original function. Successive shrinking of the original search region to which this procedure is applied leads to fairly accurate estimates, within 0.57%, of the global minima of synthetic nonconvex piecewise-quadratic functions for which the global minima are known exactly.