Convex underestimators for variational and optimal control problems
| Autor: | Paul I Bartona, Adam B. Singer, Jin-Kwang Bok |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Convex analysis
Mathematical optimization TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Convex optimization MathematicsofComputing_GENERAL MathematicsofComputing_NUMERICALANALYSIS Regular polygon Bilinear interpolation Optimal control Stationary point Convexity in economics Convexity Mathematics |
| DOI: | 10.1016/s1570-7946(01)80122-x |
| Popis: | Publisher Summary This chapter presents an overview of convexity for variational problems. These notions of convexity are then used to develop a theoretical framework for convex underestimators for variational problems. Necessary and sufficient conditions for a minimum of the convex underestimating problem are developed. Convexity is an important notion in conventional optimization schemes, because convexity implies that any stationary point found is a global minimum (the unique global minimum for strict convexity). The existence of tight convex underestimators for real functions of special form, such as univariate concave, bilinear, and trilinear functions, has long been established in the field of optimization. The fundamentals of convexity for functionals, specifically integral functionals, are presented. The theoretical groundwork is developed, enabling the derivation of convex underestimators for variational problems. Optimality conditions for constrained convex problems of special form have been developed and proven. While currently being limited only to variational problems, the future of this work will be to extend this theory to encompass the general problems of optimal control. |
| Databáze: | OpenAIRE |
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