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 On nonsmooth mathematical programs with equilibrium constraints using generalized convexity

2019 ◽  
Vol 29 (4) ◽  
pp. 449-463
Author(s):  
Bhuwan Joshi ◽  
Shashi Mishra ◽  
P Pankaj
Keyword(s):  
Generalized Convexity ◽  
Mathematical Program ◽  
Strong Duality ◽  
Global Optimality ◽  
Sufficient Condition ◽  
Equilibrium Constraints ◽  
Duality Theorems ◽  
Generalized Invexity ◽  
Mathematical Programs ◽  
Dual Models

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

scholarly journals Nondifferentiable higher order symmetric duality under invexity/generalized invexity

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1661-1674 ◽  
Author(s):  
T.R. Gulati ◽  
Khushboo Verma
Keyword(s):  
Higher Order ◽  
Duality Theorems ◽  
Symmetric Duality ◽  
Converse Duality ◽  
Generalized Invexity ◽  
Self Duality ◽  
Special Cases ◽  
Dual Models

In this paper, we introduce a pair of nondifferentiable higher-order symmetric dual models. Weak, strong and converse duality theorems for this pair are established under the assumption of higher order invexity/generalized invexity. Self duality has been discussed assuming the function involved to be skew-symmetric. Several known results are obtained as special cases.

scholarly journals Duality theorems for nondifferentiable semi-infinite interval-valued optimization problems with vanishing constraints

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haijun Wang ◽  
Huihui Wang
Keyword(s):  
Optimization Problem ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Strong Duality ◽  
Infinite Interval ◽  
Duality Theorems ◽  
Converse Duality ◽  
Vanishing Constraints ◽  
Dual Models ◽  
Interval Valued

AbstractIn this paper, we study the duality theorems of a nondifferentiable semi-infinite interval-valued optimization problem with vanishing constraints (IOPVC). By constructing the Wolfe and Mond–Weir type dual models, we give the weak duality, strong duality, converse duality, restricted converse duality, and strict converse duality theorems between IOPVC and its corresponding dual models under the assumptions of generalized convexity.

scholarly journals Generalized invexity and mathematical programs

2020 ◽  
pp. 35-35
Author(s):  
Bhuwan Joshi ◽  
Rakesh Mohan ◽  
P Pankaj
Keyword(s):  
Generalized Convexity ◽  
Strong Duality ◽  
Mathematical Programming Problem ◽  
Stationary Condition ◽  
Local Optimality ◽  
Equilibrium Constraints ◽  
Duality Theorems ◽  
Mathematical Programs ◽  
Convexity Assumptions ◽  
Dual Models

In this paper, using generalized convexity assumptions, we show that M- stationary condition is sufficient for global or local optimality under some mathematical programming problem with equilibrium constraints(MPEC). Further, we formulate and study Wolfe type and Mond-Weir type dual models for the MPEC, and we establish weak and strong duality theorems.

Capturing Electricity Market Dynamics in the Optimal Trading of Strategic Agents using Neural Network Constrained Optimization

2021 ◽  
Author(s):  
Mihály Dolányi ◽  
Kenneth Bruninx ◽  
Jean-François Toubeau ◽  
Erik Delarue
Keyword(s):  
Neural Network ◽  
Electricity Markets ◽  
Electricity Market ◽  
Mathematical Program ◽  
Market Dynamics ◽  
Equilibrium Constraints ◽  
Market Outcomes ◽  
Optimal Trading ◽  
Optimal Bidding ◽  
Upper Level

In competitive electricity markets the optimal trading problem of an electricity market agent is commonly formulated as a bi-level program, and solved as mathematical program with equilibrium constraints (MPEC). In this paper, an alternative paradigm, labeled as mathematical program with neural network constraint (MPNNC), is developed to incorporate complex market dynamics in the optimal bidding strategy. This method uses input-convex neural networks (ICNNs) to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., to replace the lower-level problem by a neural network. In a comparative analysis, the optimal bidding problem of a load agent is formulated via the proposed MPNNC and via the classical bi-level programming method, and compared against each other.

scholarly journals Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1348 ◽  
Author(s):  
Ramu Dubey ◽  
Lakshmi Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Type Model ◽  
Dual Model ◽  
Duality Theorems ◽  
Converse Duality ◽  
Numerical Example ◽  
Primal Dual

In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond–Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.

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.

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