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    TIẾN SĨ Some qualitative probilems in optimization

    Mit Barbie Mit Barbie Đang Ngoại tuyến (2263 tài liệu)
    .:: Silver Member ::.
  1. Gửi tài liệu
  2. Bình luận
  3. Chia sẻ
  4. Thông tin
  5. Công cụ
  6. Some qualitative probilems in optimization

    SOME QUALITATIVE PROBILEMS IN OPTIMIZATION

    TA QUANG SON

    Trang nhan đề
    Lời cam đoan
    Lời cảm ơn
    Mục lục
    Danh mục các ký hiệu
    Lời giới thiệu
    Chương_1: Preliminaries
    Chương_2: Optimality conditions, Lagrange duality, and stability for convex infinite problems
    Chương_3: Characterizations of solutions sets of convex infinite problems and extensions
    Chương 4: ε- Optimality and ε- Lagrangian duality for conver infinite problems
    Chương_5: ε- Optimality and ε- Lagrangian duality for non -conver infinite problems

    Kết luận và hướng phát triển

    Contents
    Half-title page i
    Honor Statement ii
    Acknowledgements iii
    Table of contents v
    Notations viii
    Introduction 1
    Chapter 1. Preliminaries 6
    1.1 Notations and basic concepts . . . . . . . . . . . . . . . . . . . . . . . 6
    1.2 Some basic results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
    1.3 Some known results concerning convex infinite problems . . . . . . . . 14
    Chapter 2. Optimality conditions, Lagrange duality, and stability of
    convex infinite problems 16
    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
    2.2 Qualification/Constraint qualification conditions . . . . . . . . . . . . . 17
    vi
    2.2.1 Relation between generalized Slater’s conditions and (FM) condition
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
    2.2.2 Relation between Slater and (FM) conditions in semi-infinite programming
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
    2.3 New version of Farkas’ lemma . . . . . . . . . . . . . . . . . . . . . . . 22
    2.4 Optimality conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
    2.5 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
    2.6 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
    Chapter 3. Characterizations of solution sets of convex infinite problems
    and extensions 37
    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
    3.2 Characterizations of solution sets of convex infinite programs . . . . . 39
    3.2.1 Characterizations of solution set via Lagrange multipliers . . . . 39
    3.2.2 Characterizations of solution set via subdifferential of Lagrangian
    function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
    3.2.3 Characterizations of solution set via minimizing sequence . . . . 45
    3.2.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
    3.3 Characterizations of solution sets of semi-convex programs . . . . . . . 48
    3.3.1 Some basic results concerning semiconvex function . . . . . . . . 49
    3.3.2 Characterizations of solution sets of semiconvex programs . . . . 52
    3.4 Characterization of solution sets of linear fractional programs . . . . . . 57
    Chapter 4. "- Optimality and "-Lagrangian duality for convex infinite
    problems 61
    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
    vii
    4.2 Approximate optimality . . . . . . . . . . . . . . . . . . . . . . . . . . 62
    4.2.1 Necessary and sufficient conditions for "-solutions . . . . . . . . 63
    4.2.2 Special case: Cone-constrained convex programs . . . . . . . . . 68
    4.3 "-Lagrangian duality and "-saddle points . . . . . . . . . . . . . . . . . 69
    4.4 Some more approximate results concerning Lagrangian function of (P) . 73
    Chapter 5. "-Optimality and "-Lagrangian duality for non-convex infinite
    problems 76
    5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
    5.2 Approximate Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
    5.3 Generalized KKT Conditions up to " . . . . . . . . . . . . . . . . . . . 81
    5.4 Quasi Saddle-Points and "-Lagrangian Duality . . . . . . . . . . . . . . 88
    Main results and open problems 94
    The papers related to the thesis 96
    Index 106
    Danh mục các công trình của tác giả
    Phụ lục
    Tài liệu tham khảo
    SOME QUALITATIVE PROBILEMS IN OPTIMIZATION

    TA QUANG SON

    Trang nhan đề
    Lời cam đoan
    Lời cảm ơn
    Mục lục
    Danh mục các ký hiệu
    Lời giới thiệu
    Chương_1: Preliminaries
    Chương_2: Optimality conditions, Lagrange duality, and stability for convex infinite problems
    Chương_3: Characterizations of solutions sets of convex infinite problems and extensions
    Chương 4: ε- Optimality and ε- Lagrangian duality for conver infinite problems
    Chương_5: ε- Optimality and ε- Lagrangian duality for non -conver infinite problems

    Kết luận và hướng phát triển

    Contents
    Half-title page i
    Honor Statement ii
    Acknowledgements iii
    Table of contents v
    Notations viii
    Introduction 1
    Chapter 1. Preliminaries 6
    1.1 Notations and basic concepts . . . . . . . . . . . . . . . . . . . . . . . 6
    1.2 Some basic results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
    1.3 Some known results concerning convex infinite problems . . . . . . . . 14
    Chapter 2. Optimality conditions, Lagrange duality, and stability of
    convex infinite problems 16
    2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
    2.2 Qualification/Constraint qualification conditions . . . . . . . . . . . . . 17
    vi
    2.2.1 Relation between generalized Slater’s conditions and (FM) condition
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
    2.2.2 Relation between Slater and (FM) conditions in semi-infinite programming
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
    2.3 New version of Farkas’ lemma . . . . . . . . . . . . . . . . . . . . . . . 22
    2.4 Optimality conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
    2.5 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
    2.6 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
    Chapter 3. Characterizations of solution sets of convex infinite problems
    and extensions 37
    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
    3.2 Characterizations of solution sets of convex infinite programs . . . . . 39
    3.2.1 Characterizations of solution set via Lagrange multipliers . . . . 39
    3.2.2 Characterizations of solution set via subdifferential of Lagrangian
    function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
    3.2.3 Characterizations of solution set via minimizing sequence . . . . 45
    3.2.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
    3.3 Characterizations of solution sets of semi-convex programs . . . . . . . 48
    3.3.1 Some basic results concerning semiconvex function . . . . . . . . 49
    3.3.2 Characterizations of solution sets of semiconvex programs . . . . 52
    3.4 Characterization of solution sets of linear fractional programs . . . . . . 57
    Chapter 4. "- Optimality and "-Lagrangian duality for convex infinite
    problems 61
    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
    vii
    4.2 Approximate optimality . . . . . . . . . . . . . . . . . . . . . . . . . . 62
    4.2.1 Necessary and sufficient conditions for "-solutions . . . . . . . . 63
    4.2.2 Special case: Cone-constrained convex programs . . . . . . . . . 68
    4.3 "-Lagrangian duality and "-saddle points . . . . . . . . . . . . . . . . . 69
    4.4 Some more approximate results concerning Lagrangian function of (P) . 73
    Chapter 5. "-Optimality and "-Lagrangian duality for non-convex infinite
    problems 76
    5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
    5.2 Approximate Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
    5.3 Generalized KKT Conditions up to " . . . . . . . . . . . . . . . . . . . 81
    5.4 Quasi Saddle-Points and "-Lagrangian Duality . . . . . . . . . . . . . . 88
    Main results and open problems 94
    The papers related to the thesis 96
    Index 106
    Danh mục các công trình của tác giả
    Phụ lục
    Tài liệu tham khảo


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