Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty

2011 ◽  
Vol 151 (2) ◽  
pp. 292-303 ◽  
Author(s):  
V. Jeyakumar ◽  
G. Y. Li
Keyword(s):  
Fractional Programming ◽  
Data Uncertainty ◽  
Robust Duality

On robust duality for fractional programming with uncertainty data

Positivity ◽  
2013 ◽  
Vol 18 (1) ◽  
pp. 9-28 ◽  
Author(s):  
Xiang -Kai Sun ◽  
Yi Chai
Keyword(s):  
Fractional Programming ◽  
Robust Duality

scholarly journals On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty

2021 ◽  
Vol 7 (2) ◽  
pp. 2331-2347
Author(s):  
Shima Soleimani Manesh ◽  
◽  
Mansour Saraj ◽  
Mahmood Alizadeh ◽  
Maryam Momeni ◽  
...  
Keyword(s):  
Objective Function ◽  
Fractional Programming ◽  
Uncertain Data ◽  
Positive Function ◽  
Efficient Solutions ◽  
Optimization Techniques ◽  
Data Uncertainty ◽  
Multi Objective ◽  
Negative Function ◽  
Function Vector

<abstract><p>In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem.</p></abstract>

scholarly journals Characterization of Robust Solution Quadratically Constrained Quadratic Optimization Problem Subjected to Data Uncertainty

2021 ◽  
pp. 1-23
Author(s):  
Moussa BARRO ◽  
Satafa SANOGO ◽  
Mohamed ZONGO ◽  
Sado TRAORÉ
Keyword(s):  
Robust Optimization ◽  
Optimization Problem ◽  
Real Life ◽  
Quadratic Optimization ◽  
Data Uncertainty ◽  
Robust Solution ◽  
Quadratic Optimization Problem ◽  
Robust Duality ◽  
Constrained Quadratic Optimization ◽  
Quadratically Constrained

Robust Optimization (RO) arises in two stages of optimization, first level for maximizing over the uncertain data and second level for minimizing over the feasible set. It is the most suitable mathematical optimization procedure to solve real-life problem models. In the present work, we characterize robust solutions for both homogeneous and non-homogeneous quadratically constrained quadratic optimization problem where constraint function and cost function are uncertain. Moreover, we discuss about optimistic dual and strong robust duality of the considered uncertain quadratic optimization problem. Finally, we complete this work with an example to illustrate our solution method. Mathematics Subject Classification: (2010) 90C20 - 90C26 - 90C46-90C47 Keywords: Robust Optimization, Data Uncertainty, Quadratic Optimization Strong Duality, Robust Solution, DPJ-Convex.

scholarly journals Robust duality for generalized convex nonsmooth vector programs with uncertain data in constraints

2021 ◽  
Author(s):  
Izhar Ahmad ◽  
Arshpreet Kaur ◽  
Mahesh Kumar Sharma
Keyword(s):  
Robust Optimization ◽  
Dual Problem ◽  
Mathematical Program ◽  
Uncertain Data ◽  
Data Uncertainty ◽  
Sufficient Optimality Conditions ◽  
Duality Theorems ◽  
Generalized Convex Functions ◽  
Robust Duality ◽  
Mathematical Problems

Robust optimization has come out to be a potent approach to study mathematical problems with data uncertainty. We use robust optimization to study a nonsmooth nonconvex mathematical program over cones with data uncertainty containing generalized convex functions. We study sufficient optimality conditions for the problem. Then we construct its robust dual problem and provide appropriate duality theorems which show the relation between uncertainty problems and their corresponding robust dual problems.

Robust duality for generalized convex programming problems under data uncertainty

2012 ◽  
Vol 75 (3) ◽  
pp. 1362-1373 ◽  
Author(s):  
V. Jeyakumar ◽  
G. Li ◽  
G.M. Lee
Keyword(s):  
Convex Programming ◽  
Data Uncertainty ◽  
Robust Duality

scholarly journals Global optimality conditions and duality theorems for robust optimal solutions of optimization problems with data uncertainty, using underestimators

2022 ◽  
Vol 12 (1) ◽  
pp. 93
Author(s):  
Jutamas Kerdkaew ◽  
Rabian Wangkeeree ◽  
Rattanaporn Wangkeeree
Keyword(s):  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Data Uncertainty ◽  
Global Optimality ◽  
Optimal Solutions ◽  
Duality Theorems ◽  
Uncertain Optimization ◽  
Kkt Point ◽  
Robust Duality

<p style='text-indent:20px;'>In this paper, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.</p>

Monetary Policy and Data Uncertainty

2005 ◽  
Author(s):  
Jarkko P. P. Jääskelä ◽  
Anthony Yates
Keyword(s):  
Monetary Policy ◽  
Data Uncertainty

Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2557-2574 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Saddle Point ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Equality Constraints ◽  
New Class ◽  
Minimax Fractional Programming

Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.

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