scholarly journals Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition

2011 ◽  
Vol 152 (3) ◽  
pp. 710-726 ◽  
Author(s):  
Guoyin Li
Keyword(s):  
Optimality Condition ◽  
Global Optimality ◽  
Quadratic Minimization ◽  
Global Optimality Condition ◽  
Necessary And Sufficient ◽  
Bivalent Constraints

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 Quadratic problems with two quadratic constraints: convex quadratic relaxation and strong Lagrangian duality

2020 ◽  
Author(s):  
Abdelouahed Hamdi ◽  
Akram Taati ◽  
Temadher A Almaadeed
Keyword(s):  
Sufficient Conditions ◽  
Optimal Solution ◽  
Lagrangian Duality ◽  
Global Optimality ◽  
Global Optimal Solution ◽  
Quadratic Constraints ◽  
Quadratic Minimization ◽  
Global Optimal ◽  
Necessary And Sufficient ◽  
Convex Quadratic Relaxation

In this paper,  we study  a nonconvex quadratic minimization problem with two quadratic constraints, one of which being convex.  We introduce two convex quadratic relaxations (CQRs) and discuss cases, where the problem is equivalent to exactly one of the CQRs. Particularly, we show that the global optimal  solution can be recovered from an optimal solution of the CQRs. Through this equivalence, we introduce new conditions under which the problem enjoys strong Lagrangian duality, generalizing  the recent  condition  in the literature.  Finally, under the new conditions,  we present  necessary and sufficient conditions for global optimality of the problem.

On Sufficient Global Optimality Conditions for Bivalent Quadratic Programs with Quadratic Constraints

2015 ◽  
Vol 32 (04) ◽  
pp. 1550025
Author(s):  
Yu-Jun Gong ◽  
Yong Xia
Keyword(s):  
Optimization Problem ◽  
Sufficient Conditions ◽  
Global Optimality ◽  
Dual Model ◽  
Zero Duality Gap ◽  
Quadratic Constraints ◽  
Quadratic Optimization Problem ◽  
Lagrangian Dual ◽  
Dual Bound ◽  
Global Optimality Condition

We show the recent sufficient global optimality condition for the quadratic constrained bivalent quadratic optimization problem is equivalent to verify the zero duality gap. Then, based on the optimal parametric Lagrangian dual model, we establish improved sufficient conditions by strengthening the dual bound.

scholarly journals Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaomei Zhang ◽  
Yanjun Wang ◽  
Weimin Ma
Keyword(s):  
Optimality Conditions ◽  
Minimization Problem ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Box Constraints ◽  
Global Minimizers ◽  
Quadratic Minimization ◽  
Binary Constraints

We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006). The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006) and Y. Wang et al. (2010). Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.

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