Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 11, Issue 2, Pages 464-494Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1052623499359828
Keywords
monotonicity; global optimization; increasing functions; normal sets; polyblock approximation algorithms; difference of increasing functions; multiplicative programming; polynomial programming; nonconvex quadratic programming; distance geometry
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Problems of maximizing or minimizing monotonic functions of n variables under monotonic constraints are discussed. A general framework for monotonic optimization is presented in which a key role is given to a property analogous to the separation property of convex sets. The approach is applicable to a wide class of optimization problems, including optimization problems dealing with functions representable as differences of increasing functions (d.i. functions).
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