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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 4

Weak-stability and saddle point theorems for a multiobjective optimization problem with an infinite number of constraints

Ta Quang SON
Ching Feng WEN
Sayfa
1953–1966
Yayın Tarihi
2022-11-04
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Connectionsbetween weak-stability and saddle point theorems of the problems are established.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we focus on weak-stability and saddle point theorems of multiobjective optimization problemsthat have an infinite number of constraints.
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Temel Bulgular & Veri:The obtained results are based on the notion of weak-subdifferentials forvector functions.
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Sonuç & Katkı:Connectionsbetween weak-stability and saddle point theorems of the problems are established.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we focus on weak-stability and saddle point theorems of multiobjective optimization problemsthat have an infinite number of constraints. The obtained results are based on the notion of weak-subdifferentials forvector functions. Some properties of weak stability for the problems are introduced. Relationships between strong dualityand saddle points of the augmented Lagrange vector functions associated to the problems are investigated. Connectionsbetween weak-stability and saddle point theorems of the problems are established. An example is given.

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Bu Makaleye Atıf Yap

SON, T. Q., WEN, C. F. (2022). Weak-stability and saddle point theorems for a multiobjective optimization problem with an infinite number of constraints. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 1953–1966. https://ajindex.com/articles/608073

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Kaynakça (16)

  1. Azimov AY, Gasimov RN. On weak conjugacy, weak subdifferentials and duality with zero gap in nonconvex optimization. International Journal of Applied Mathematics 1999; 4: 171-192
  2. Azimov AY, Gasimov RN. Stability and duality of nonconvex problems via augmented Lagrangian. Cybernetics and Systems Analysis 2002; 38: 412-421
  3. Clarke FH. Generalized gradient and applications. Transactions of the American Mathematical Society 1975; 205: 247-262
  4. Gasimov RN. Augmented Lagrangian duality and nondifferentiable optimization methods in nonconvex programming. Journal of Global Optimization 2002; 24: 187-203
  5. Gasimov RN, Rubinov AM. On augmented Lagrangians for optimization problems with a single constraint. Journal of Global Optimization 2004; 28: 153-173
  6. Kasımbeyli R, İnceoğlu G. The properties of the weak subdifferentials. Gazi University Journal of Science 2010; 23: 49-52
  7. Kasimbeyli R, Mamadov M. On weak subdifferentials, directional derivatives and radial epiderivatives for nonconvex functions. SIAM Journal on Optimization 2009; 20: 841-855
  8. Kasimbeyli R, Mamadov M. Optimality conditions in nonconvex optimization via weak subdifferentials. Nonlinear Analysis 2011; 74: 2534-2547
  9. Küçük Y, Ataserver I, Küçük M. Generalized weak subdifferentials. Optimization 2011; 60: 537-552
  10. Küçük Y, Ataserver I, Küçük M. Weak Fenchel and weak Fenchel-Lagrange conjugate duality for nonconvex scalar optimization problems. Journal of Global Optimization 2012; 54: 813-830
  11. Mordukhovich BS, Shao Y. On nonconvex subdifferentials calculus in Banach spaces. Journal of Convex Analysis 1995; 2: 211-227
  12. Rockafellar RT. Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization. Mathematics of Operations Research 1981; 6: 424-436
  13. Rockafellar RT. The Theory of Subgradients and Its Applications to Problems of Optimization: Convex and Nonconvex Functions. Berlin, Germany: Helderman, 1981
  14. Rockafellar RT. Extensions of subgradient calculus with applications in optimization. Nonlinear Analysis 1985; 9: 665-698
  15. Son TQ, Kim DS, Tam NN. Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian. Journal of Global Optimization 2012; 53: 163-184
  16. Son TQ, Wen CF. Weak-subdifferentials for vector functions and applications to multiobjective semi-infinite optimization problems. Applicable Analysis (in press). doi: 10.1080/00036811.2018.1514018 [17] Walk M