A new necessary and sufficient global optimality condition for canonical DC problems

2012 ◽  
Vol 55 (3) ◽  
pp. 559-577 ◽  
Author(s):  
Qinghua Zhang
Keyword(s):  
Optimality Condition ◽  
Global Optimality ◽  
Global Optimality Condition ◽  
Necessary And Sufficient ◽  
Dc Problems

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.

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 Bilevel programs with extremal value function: global optimality

2005 ◽  
Vol 2005 (3) ◽  
pp. 419-435 ◽  
Author(s):  
Abdelmalek Aboussoror ◽  
Hicham Babahadda ◽  
Abdelatif Mansouri
Keyword(s):  
Value Function ◽  
Convex Set ◽  
Maximization Problem ◽  
Global Optimality ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bilevel Program ◽  
Bilevel Programs ◽  
Necessary And Sufficient ◽  
Extremal Value

For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to amax-minproblem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over a convex set. Finally, this case is completed by an algorithm.

scholarly journals Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2355
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Type Inequality ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Global Optimality ◽  
Fractional Operators ◽  
Fractional Optimal Control ◽  
Analytic Kernel ◽  
Global Optimality Condition

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed.

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