Global optimality condition for quadratic optimization problems under data uncertainty

Positivity ◽  
2021 ◽  
Author(s):  
Moussa Barro ◽  
Ali Ouedraogo ◽  
Sado Traore
Keyword(s):  
Optimality Condition ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Data Uncertainty ◽  
Global Optimality ◽  
Global Optimality Condition

scholarly journals Some remarks on duality and optimality of a class of constrained convex quadratic minimization problems

2017 ◽  
Vol 27 (2) ◽  
pp. 219-225
Author(s):  
Sudipta Roy ◽  
Sandip Chatterjee ◽  
R.N. Mukherjee
Keyword(s):  
Optimality Condition ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Global Optimality ◽  
Convex Quadratic Optimization ◽  
Quadratic Minimization ◽  
Minimization Problems ◽  
Global Optimality Condition

In this paper the duality and optimality of a class of constrained convex quadratic optimization problems have been studied. Furthermore, the global optimality condition of a class of interval quadratic minimization problems has also been discussed.

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>

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

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