Global optimality condition and fixed point continuation algorithm for non-Lipschitz ℓ p regularized matrix minimization

2018 ◽  
Vol 61 (6) ◽  
pp. 1139-1152
Author(s):  
Dingtao Peng ◽  
Naihua Xiu ◽  
Jian Yu
Keyword(s):  
Fixed Point ◽  
Optimality Condition ◽  
Global Optimality ◽  
Global Optimality Condition ◽  
Continuation Algorithm

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 A global optimality result using Geraghty type contraction

2014 ◽  
Vol 4 (2) ◽  
pp. 99-104 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Pranati Maity ◽  
P. Konar
Keyword(s):  
Fixed Point ◽  
Best Approximation ◽  
Approximate Solutions ◽  
Global Optimality ◽  
Approximation Theorems ◽  
The Best Approximation ◽  
Optimal Values ◽  
Type Contraction

In this paper we prove two proximity point results for finding the distance between two sets. Unlike the best approximation theorems they provide with globally optimal values. Here our approach is to reduce the problem to that of finding optimal approximate solutions of some fixed point equations. We use Geraghty type contractive inequalities in our theorem. Two illustrative examples are given.

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.

scholarly journals On the optimality of double-bracket flows

2004 ◽  
Vol 2004 (62) ◽  
pp. 3301-3319 ◽  
Author(s):  
Anthony M. Bloch ◽  
Arieh Iserles
Keyword(s):  
Fixed Point ◽  
Global Optimality ◽  
Stable Fixed Point ◽  
Different Types

We analyze the optimality of the stable fixed point of the double-bracket equations. We introduce different types of optimality and prove local and global optimality results with respect to the Schattenp-norms.

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