Book
Convex Optimization in Infinite Dimensional Spaces.
| Title: | Convex Optimization in Infinite Dimensional Spaces. |
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| Authors: | Morari, Manfred, Thoma, Manfred, Blondel, Vincent D., Boyd, Stephen P., Kimura, Hidenori, Mitter, Sanjoy K. |
| Source: | Recent Advances in Learning & Control; 2008, p161-179, 19p |
| Abstract: | The duality approach to solving convex optimization problems is studied in detail using tools in convex analysis and the theory of conjugate functions. Conditions for the duality formalism to hold are developed which require that the optimal value of the original problem vary continuously with respect to perturbations in the constraints only along feasible directions; this is sufficient to imply existence for the dual problem and no duality gap. These conditions are also posed as certain local compactness requirements on the dual feasibility set, based on a characterization of locally compact convex sets in locally convex spaces in terms of nonempty relative interiors of the corresponding polar sets. The duality theory and related convex analysis developed here have applications in the study of Bellman-Hamilton Jacobi equations and Optimal Transportation problems. See Fleming-Soner [8] and Villani [9]. [ABSTRACT FROM AUTHOR] |
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| DOI: | 10.1007/978-1-84800-155-8_12 |
| Database: | Complementary Index |
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