Foundations of a strong monotonicity theorem

Douglass J. Wilde

doi:10.1117/12.235508

22 March 1996 Foundations of a strong monotonicity theorem

Douglass J. Wilde

Proceedings Volume 2644, Fourth International Conference on Computer-Aided Design and Computer Graphics; (1996) https://doi.org/10.1117/12.235508
Event: Fourth International Conference on Computer-Aided Design and Computer Graphics, 1995, Wuhan, China

Abstract

Current monotonicity analysis of optimization problems has loose ends and loopholes which confuse the understanding, teaching and use of the techniques. These embarrassments are removed in this article by redefining slightly the domain, the objective and constraint functions, and even the notion of criticality itself. This leads to a simple and clear `Strong' Monotonicity Theorem giving extensions of the two monotonicity principles are straightforward corollaries. This theorem not only incorporates Hansen, Jaumard and Lu's extensions to non-monotonic functions, but also clarifies the special elimination rules applicable to variables in the constraints but not the objective. This sets the stage for analyzing optimization problems with non-monotonic functions.

Citation Download Citation

Douglass J. Wilde "Foundations of a strong monotonicity theorem", Proc. SPIE 2644, Fourth International Conference on Computer-Aided Design and Computer Graphics, (22 March 1996); https://doi.org/10.1117/12.235508

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