On optimality and duality theorems of nonlinear disjunctive fractional minmax programs

2007 ◽  
Vol 180 (3) ◽  
pp. 971-982 ◽  
Author(s):  
E.E. Ammar
Keyword(s):  
Duality Theorems ◽  
Optimality And Duality

scholarly journals Optimality and duality for nonsmooth semi-infinite E-convex multi-objective programming with support functions

2020 ◽  
Vol 11 ◽  
pp. 17
Author(s):  
Tarek Emam
Keyword(s):  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Convex Programming Problem ◽  
Duality Theorems ◽  
Support Functions ◽  
Primal Problem ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Convexity Assumptions

In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak and strong duality theorems under various generalized E-convexity assumptions.

scholarly journals Optimality and Duality with Respect to b-(E,m)-Convex Programming

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 774
Author(s):  
Bo Yu ◽  
Jiagen Liao ◽  
Tingsong Du
Keyword(s):  
Convex Programming ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Convex Mappings ◽  
Uniqueness Of The Solution ◽  
Optimality And Duality

Noticing that E -convexity, m-convexity and b-invexity have similar structures in their definitions, there are some possibilities to treat these three class of mappings uniformly. For this purpose, the definitions of the ( E , m ) -convex sets and the b- ( E , m ) -convex mappings are introduced. The properties concerning operations that preserve the ( E , m ) -convexity of the proposed mappings are derived. The unconstrained and inequality constrained b- ( E , m ) -convex programming are considered, where the sufficient conditions of optimality are developed and the uniqueness of the solution to the b- ( E , m ) -convex programming are investigated. Furthermore, the sufficient optimality conditions and the Fritz–John necessary optimality criteria for nonlinear multi-objective b- ( E , m ) -convex programming are established. The Wolfe-type symmetric duality theorems under the b- ( E , m ) -convexity, including weak and strong symmetric duality theorems, are also presented. Finally, we construct two examples in detail to show how the obtained results can be used in b- ( E , m ) -convex programming.

scholarly journals Optimality and duality without a constraint qualification for minimax programming

2003 ◽  
Vol 67 (1) ◽  
pp. 121-130 ◽  
Author(s):  
Houchun Zhou ◽  
Wenyu Sun
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Dual Model ◽  
Duality Theorems ◽  
Minimax Programming ◽  
Optimality And Duality ◽  
Necessary And Sufficient

Without the need of a constraint qualification, we establish the optimality necessary and sufficient conditions for generalised minimax programming. Using these optimality conditions, we construct a parametric dual model and a parameter-free mixed dual model. Several duality theorems are established.

scholarly journals Optimality and duality for complex multi-objective programming

2022 ◽  
Vol 12 (1) ◽  
pp. 121
Author(s):  
Tone-Yau Huang ◽  
Tamaki Tanaka
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Dual Model ◽  
Duality Theorems ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Objective Programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

scholarly journals Optimality and duality for nonsmooth semi-infinite mathematical program with equilibrium constraints involving generalized invexity of order σ > 0  

2020 ◽  
Author(s):  
Bhuwan Chandra Joshi
Keyword(s):  
Mathematical Program ◽  
Global Optimality ◽  
Sufficient Condition ◽  
Equilibrium Constraints ◽  
Duality Theorems ◽  
Converse Duality ◽  
Generalized Invexity ◽  
Optimality And Duality ◽  
Dual Models

In this paper, we derive sufficient condition for global optimality for a nonsmooth semi-infinite mathematical program with equilibrium constraints involving generalized invexity of order  σ > 0   assumptions. We formulate the Wolfe and Mond-Weir type dual models for the problem using convexificators. We establish weak, strong and strict converse duality theorems to relate the semi-infinite mathematical program with equilibrium constraints and the dual models in the framework of convexificators.

scholarly journals Optimality and duality for nonsmooth semi-infinite multiobjective programming with support functions

2017 ◽  
Vol 27 (2) ◽  
pp. 205-218 ◽  
Author(s):  
Yadvendra Singh ◽  
S.K. Mishra ◽  
K.K. Lai
Keyword(s):  
Generalized Convexity ◽  
Multiobjective Programming ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Support Functions ◽  
Primal Problem ◽  
Special Cases ◽  
Multiobjective Programming Problem ◽  
Optimality And Duality ◽  
Convexity Assumptions

In this paper, we consider a nonsmooth semi-infinite multiobjective programming problem involving support functions. We establish sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak, strong and strict converse duality theorems under various generalized convexity assumptions. Moreover, some special cases of our problem and results are presented.

scholarly journals ON OPTIMALITY AND DUALITY IN INTERVAL-VALUED VARIATIONAL PROBLEM WITH B-(p,r)-INVEXITY

2021 ◽  
Author(s):  
Indira Priyadarshini Debnath ◽  
Nisha Pokharna
Keyword(s):  
Variational Problem ◽  
Optimization Problem ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Real World Problem ◽  
Sufficiency Theorem ◽  
Optimality And Duality ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Interval Valued

In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition of B -( p,r )- invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established under B -( p,r )-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for an interval- optimization problem Mond-Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.

Sign in / Sign up

Export Citation Format

Share Document