文摘
英文文摘
致谢
详细中文摘要
1 Introduction
2 Notations and preliminaries
3 Fechel duality for convex optimization problems and for DC problems
3.1 Stable and total Fenchel duality for convex optimization problems
3.1.1 Introduction
3.1.2 New regularity conditions
3.1.3 Stable Fenchel duality
3.1.4 Stable Total Fenchel duality
3.1.5 Converse Fenchel duality
3.2 Stable and total Fenchel duality for DC optimization problems
3.2.1 Introduction
3.2.2 The condition(FRC)A and strong dualities
3.2.3 The condition(CC)A and stable strong dualities
3.2.4 Moreau-Rockafellar formula and total dualities
4 Lagrange duality for convex infinite programming and DC infinite programming
4.1 Extended Farkas's lemmas and Lagrangian dualities in convex infinite programming
4.1.1 Introduction
4.1.2 New regularity conditions
4.1.3 Extended Farkas Lemmas
4.1.4 Strong Lagrangian dualities
4.1.5 Applications to Conic Programming
4.2 Optimality conditions and total Lagrange dualities in convex infinite programming
4.2.1 Introduction
4.2.2 New regularity condition
4.2.3 Optimality conditions
4.2.4 Total Lagrange dualities
4.2.5 Applications to conic programming
4.3 Lagrangian dualities and extended Farkas's lemma for DC infinite programming
4.3.1 Introduction
4.3.2 The weak duality and the strong duality
4.3.3 The stable strong dualities
4.3.4 Farkas Lemma for DC programming
4.3.5 The total Lagrange dualities
4.3.6 Optimality conditions
5 Conclusions
BIBLIOGRAPHY
简历
读博期间发表的论文
