Convex sub-differential sum rule via convex semi-closed functions with applications in convex programming |
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| Authors: | Mohsen Alimohammady Yeol Je Cho Vahid Dadashi Mehdi Roohi |
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| Affiliation: | 1. Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran;2. Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea;3. Islamic Azad University, Sari Branch, Sari, Iran |
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| Abstract: | This paper deals with some basic notions of convex analysis and convex optimization via convex semi-closed functions. A decoupling-type result and also a sandwich theorem are proved. As a consequence of the sandwich theorem, we get a convex sub-differential sum rule and two separation results. Finally, the derived convex sub-differential sum rule is applied to solving the convex programming problem. |
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