Multiobjective optimization problems with modified objective functions and cone constraints and applications

Chen, Jia Wei; Cho, Yeol Je; Kim, Jong Kyu; Li, Jun

doi:10.1007/s10898-010-9539-3

Cited by 37 publications

(16 citation statements)

References 16 publications

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“…(iii) If we replace m by k, p by m, the function g by q : R n → R and if we take K = R k + and Q = S, then our problem (FP) reduces to the problem (MFP) considered by Chen et al [20].…”

Section: Optimality Conditionsmentioning

confidence: 99%

Higher order optimality and duality in fractional vector optimization over cones

Kapoor¹,

Suneja²,

Grover³

2017

Tamkang J. Math.

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“…(iii) If we replace m by k, p by m, the function g by q : R n → R and if we take K = R k + and Q = S, then our problem (FP) reduces to the problem (MFP) considered by Chen et al [20].…”

Section: Optimality Conditionsmentioning

confidence: 99%

Higher order optimality and duality in fractional vector optimization over cones

Kapoor¹,

Suneja²,

Grover³

2017

Tamkang J. Math.

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“…Our results in this paper are different from any existence theorems for equilibrium problems in the literatures. See for example, one can refer [1][2][3][5][6][7][8]16,18,19,30,31] and references therein.…”

Section: ϕ(R )D(x T X) ≤ D(x Y) Implies That D(t X T Y) ≤ αD(x T mentioning

confidence: 99%

Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications

Chuang

Lin

2012

J Glob Optim

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In this paper, we presented new and important existence theorems of solution for quasi-equilibrium problems, and we show the uniqueness of its solution which is also a fixed point of some mapping. We also show that this unique solution can be obtained by Picard's iteration method. We also get new minimax theorem, and existence theorems for common solution of fixed point and optimization problem on complete metric spaces. Our results are different from any existence theorems for quasi-equilibrium problems and minimax theorems in the literatures.

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“…The weakly efficient (weak minimum) solution is one of the most efficient solution concepts in mathematical models, economics, decision theory, optimal control and game theory, see, [17]. The necessary and sufficient optimality conditions for multiobjective optimization problems (MOP) were deeply studied and attained a lot of research achievement during the last decades; See, for example, [2,4,13,14,18] and the references therein. Despite the existence of multiple efficient solutions, in practice, usually only one of these solutions is to be chosen.…”

Section: Introductionmentioning

confidence: 99%

A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

et al. 2016

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By using auxiliary principle technique, a new proximal point algorithm based on decomposition method is suggested for computing a weakly efficient solution of the constrained multiobjective optimization problem (MOP) without assuming the nonemptiness of its solution set. The optimality conditions for (MOP) are derived by the Lagrangian function of its subproblem and corresponding mixed variational inequality. Some basic properties and convergence results of the proposed method are established under some mild assumptions. As an application, we employ the proposed method to solve a split feasibility problem. Finally, numerical results are also presented to illustrate the feasibility of the proposed algorithm.

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Multiobjective optimization problems with modified objective functions and cone constraints and applications

Abstract: Multiobjective optimization problem, Q-(pseudo)invex, Q-convexlike, Weakly efficient solution, Saddlepoint, KKT condition, Weak (strong, converse) duality, Lagrange function, 90C29, 90C46, 47J20,

Cited by 37 publications

References 16 publications

Higher order optimality and duality in fractional vector optimization over cones

Higher order optimality and duality in fractional vector optimization over cones

Existence and uniqueness of solution for quasi-equilibrium problems and fixed point problems on complete metric spaces with applications

A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

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