Necessary and sufficient conditions for the inequality constrained optimization problem using directional derivatives †

1972 ◽  
Vol 3 (3) ◽  
pp. 263-275
Author(s):  
ROBERT N. BRASWELL ◽  
JORGE A. MARBAN
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Directional Derivatives ◽  
Constrained Optimization Problem ◽  
Inequality Constrained Optimization ◽  
Necessary And Sufficient

scholarly journals Invexity of supremum and infimum functions

2002 ◽  
Vol 65 (2) ◽  
pp. 289-306 ◽  
Author(s):  
Nguyen Xuan Ha ◽  
Do Van Luu
Keyword(s):  
Sufficient Conditions ◽  
Infinite Family ◽  
Lipschitz Functions ◽  
Necessary And Sufficient Conditions ◽  
Directional Derivatives ◽  
Mathematical Programs ◽  
Sufficient Conditions For Optimality ◽  
Invex Function ◽  
Necessary And Sufficient

Under suitable assumptions we establish the formulas for calculating generalised gradients and generalised directional derivatives in the Clarke sense of the supremum and the infimum of an infinite family of Lipschitz functions. From these results we derive the results ensuring such a supremum or infimum are an invex function when all functions of the invex. Applying these results to a class of mathematical programs, we obtain necessary and sufficient conditions for optimality.

scholarly journals Linear-quadratic optimization and some general hypotheses on optimal control

1999 ◽  
Vol 5 (4) ◽  
pp. 275-289 ◽  
Author(s):  
L. I. Rozonoer
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Quadratic Optimization ◽  
Necessary And Sufficient Conditions ◽  
Maximum Condition ◽  
Linear Quadratic ◽  
Existence Of Optimal Control ◽  
Necessary And Sufficient

Necessary and sufficient conditions for existence of optimal control for all initial data are proved forLQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.

scholarly journals Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Zhe Chen
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Solution Set ◽  
Asymptotic Cone ◽  
Convex Optimization Problem ◽  
Composite Optimization ◽  
Convex Composite Optimization ◽  
Necessary And Sufficient

We characterize the asymptotic cone of the solution set of a convex composite optimization problem. We then apply the obtained results to study the necessary and sufficient conditions for the nonemptiness and compactness of the solution set of the problem. Our results generalize and improve some known results in literature.

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