On stationarity for nonsmooth multiobjective problems with vanishing constraints

In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type constraints qualification to achieve strong S—stationary conditions from Fritz John stationary conditions. Further, we establish strong S—stationary necessary and sufficient conditions, independently from Fritz John conditions. The optimality results for multiobjective semidefinite optimization problem in this paper is related to two recent articles by Treanta in 2021. Treanta in 2021 discussed duality theorems for special class of quasiinvex multiobjective optimization problems for interval-valued components. The study in our article can also be seen and extended for the interval-valued optimization motivated by Treanta (2021). Some examples are provided to validate our established results.

show abstract

“…Motivated by Achtziger and Kanzow [12] and Sadeghieh et al [55], we define Sstationary point for S-MMPVC. Definition 8.…”

Section: Definition 7 the Generalized Guignard Constraint Qualificati...mentioning

confidence: 99%

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In [6], strong KKT necessary optimality conditions for multiobjective mathematical programming problems with vanishing constraints were explored. The papers [7,8] studied some constraint qualifications in terms of Clarke subdifferentials and applied them in establishing the KKT optimality conditions for nonsmooth mathematical programming problems. Some results on the duality for mathematical programming problems with vanishing constraints were discussed in [9,10].…”

Section: Introductionmentioning

confidence: 99%

Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints

2022

Appl. Set-Valued Anal. Optim.

View full text Add to dashboard Cite

This paper considers the nonsmooth multiobjective semi-infinite programming problems with vanishing constraints. Using Clarke subdifferentials, we first obtain both necessary and sufficient Karush-Kuhn-Tucker optimality conditions for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints. Then, the duality relations of types of Wolfe and Mond-Weir dual problems are explored under convexity assumptions.

show abstract

“…Two Abadie-type constraint qualifications were introduced and some necessary conditions for Geoffrion properly efficient solutions were given by convex subdifferentials. Recently in [18], for the nonsmooth MMPVCs, some data qualifications characterized by Clarke subdifferential were introduced, and the relationship among them was discussed. Some stationary conditions as necessary or sufficient conditions of weakly efficient and Pareto efficient solutions were also given.…”

Section: Introductionmentioning

confidence: 99%

“…Some stationary conditions as necessary or sufficient conditions of weakly efficient and Pareto efficient solutions were also given. Motivated by [18], it is natural for us to consider the stationary condition for Borwein proper efficient solutions of the MMPVC.…”

Section: Introductionmentioning

confidence: 99%

Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints

Huang

Zhu

2022

Mathematics

View full text Add to dashboard Cite

This paper discusses optimality conditions for Borwein proper efficient solutions of nonsmooth multiobjective optimization problems with vanishing constraints. A new notion in terms of contingent cone and upper directional derivative is introduced, and a necessary condition for the Borwein proper efficient solution of the considered problem is derived. The concept of ε proper Abadie data qualification is also introduced, and a necessary condition which is called a strictly strong stationary condition for Borwein proper efficient solutions is obtained. In view of the strictly strong stationary condition, convexity of the objective functions, and quasi-convexity of constrained functions, sufficient conditions for the Borwein proper efficient solutions are presented. Some examples are given to illustrate the reasonability of the obtained results.

show abstract

On stationarity for nonsmooth multiobjective problems with vanishing constraints

Cited by 11 publications

References 20 publications

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints

Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints

Contact Info

Product

Resources

About