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Supports and convex envelopes |
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| Authors: | Stephen J. Grotzinger |
| Affiliation: | (1) Department of Mathematical Sciences, George Mason University, 4400 University Drive, 22030 Fairfax, VA, USA |
| Abstract: | The construct of anL 1-Support is extended to the environment of a lower semicontinuous function over a solid, finite union of polytopes by utilizing the convex envelope of the function. The existence of and a characterization for theL 1-Support of the convex envelope are established. The characterization is solely dependent upon the original function’s characteristics and thus the need to calculate the functional form of the convex envelope explicity is eliminated. |
| Keywords: | Centroid Conjugate Function Convex Envelope Convex Hull Global Optimization Locally Simplicial Set L 1-Support Lower Semicontinuous Function Semi-Infinite Programming Separable Optimization Problem Subdifferential Subgradient |
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