• The Pure and Applied Mathematics
• /
• v.15 no.2
• /
• pp.203-207
• /
• 2008

In [1], Mishra and Wang established relationships between vector variational-like inequality problems and non-smooth vector optimization problems under non-smooth invexity in finite-dimensional spaces. In this paper, we generalize recent results of Mishra and Wang to infinite-dimensional case.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1527-1534
• /
• 2010

In this paper, we consider nonsmooth optimization problem of which objective and constraint functions are locally Lipschitz. We establish sufficient optimality conditions and duality results for nonsmooth vector optimization problem given under nearly strict invexity and near invexity-infineness assumptions.

• East Asian mathematical journal
• /
• v.33 no.1
• /
• pp.83-102
• /
• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.3
• /
• pp.475-496
• /
• 2021

The main aim is to define a new class of generalized h-variational inequality problems and its generalized h-variational inequality problems. We define the class of h-𝜂-invex set, h-𝜂-invex function and H-pseudospace. Existence of the solution of the problems are established in H-pseudospace with the help of H-KKM mapping theorem and HC_*-condition of 𝜂 associated with the function h.

• East Asian mathematical journal
• /
• v.32 no.5
• /
• pp.635-639
• /
• 2016

In this paper, we prove a sufficient optimality theorems for the problem(FP) under(V, ${\rho}$)-invexity assumption. And we give Mond-Weir type dual problem and proved weak and strong duality theorem under (V, ${\rho}$)-invexity

• East Asian mathematical journal
• /
• v.33 no.3
• /
• pp.265-269
• /
• 2017

In this paper, we formulate a sufficient optimality theorem for the robust optimization problem (UP) under (V, ${\rho}$)-invexity assumption. Moreover, we formulate a Mond-Weir type dual problem for the robust optimization problem (UP) and show that the weak and strong duality hold between the primal problems and the dual problems.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.539-551
• /
• 2005

In this paper, sufficient optimality conditions and duality results for nonsmooth vector optimization problems are given under near invexity and infineness assumptions. Also, weak vector saddle-point theorems are obtained under near invexity-infineness assumptions.

• Communications of the Korean Mathematical Society
• /
• v.20 no.4
• /
• pp.837-847
• /
• 2005

We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.