A Lagrange duality approach for multi-composed optimization problems
| Autor: | Gert Wanka, Oleg Wilfer |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Mathematical optimization 021103 operations research Information Systems and Management Optimization problem Duality gap 010102 general mathematics 0211 other engineering and technologies Duality (optimization) Perturbation function 02 engineering and technology Management Science and Operations Research 01 natural sciences Weak duality Modeling and Simulation Discrete Mathematics and Combinatorics Strong duality Wolfe duality 0101 mathematics Interior point method Mathematics |
| Zdroj: | TOP. 25:288-313 |
| ISSN: | 1863-8279 1134-5764 |
| DOI: | 10.1007/s11750-016-0431-2 |
| Popis: | In this paper, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of $$n+1$$ functions. For this problem, we calculate its conjugate dual problem, where the functions involved in the objective function of the primal problem will be decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach, we determine the formulas of the conjugate as well as the biconjugate of the objective function of the primal problem and discuss an optimization problem having as objective function the sum of reciprocals of concave functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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