Optimality condition and quasi-conjugate duality with zero gap in nonconvex optimization

2019 ◽  
Vol 14 (8) ◽  
pp. 2021-2037
Author(s):  
Pham Ngoc Anh ◽  
Tran Van Thang
Keyword(s):  
Optimality Condition ◽  
Nonconvex Optimization ◽  
Conjugate Duality ◽  
Duality With Zero Gap

scholarly journals Robust strong duality for nonconvex optimization problem under data uncertainty in constraint

2021 ◽  
Vol 6 (11) ◽  
pp. 12321-12338
Author(s):  
Yanfei Chai ◽  
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problem ◽  
Conjugate Function ◽  
Strong Duality ◽  
Data Uncertainty ◽  
Abstract Convexity ◽  
Conjugate Duality ◽  
Dual Problems ◽  
Uncertain Optimization ◽  
Robust Strong Duality

<abstract><p>This paper deals with the robust strong duality for nonconvex optimization problem with the data uncertainty in constraint. A new weak conjugate function which is abstract convex, is introduced and three kinds of robust dual problems are constructed to the primal optimization problem by employing this weak conjugate function: the robust augmented Lagrange dual, the robust weak Fenchel dual and the robust weak Fenchel-Lagrange dual problem. Characterizations of inequality (1.1) according to robust abstract perturbation weak conjugate duality are established by using the abstract convexity. The results are used to obtain robust strong duality between noncovex uncertain optimization problem and its robust dual problems mentioned above, the optimality conditions for this noncovex uncertain optimization problem are also investigated.</p></abstract>

A Class of Decision Processes Showing Policy-Improvement/Newton–Raphson Equivalence

1989 ◽  
Vol 3 (3) ◽  
pp. 397-403 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Optimality Condition ◽  
Regularity Condition ◽  
Decision Processes ◽  
Policy Improvement ◽  
Improvement Algorithm ◽  
Newton Raphson ◽  
Raphson Algorithm

A condition expressed in Eq. (7) is given which, with one simplifying regularity condition, ensures that the policy-improvement algorithm is equivalent to application of the Newton–Raphson algorithm to an optimality condition. It is shown that this condition covers the two known cases of such equivalence, and another example is noted. The condition is believed to be necessary to within transformations of the problem, but this has not been proved.

Derivatives of Hadamard type in vector optimization

2018 ◽  
Vol 68 (2) ◽  
pp. 421-430
Author(s):  
Karel Pastor
Keyword(s):  
Nonlinear Analysis ◽  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimality Condition ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Dini Derivatives ◽  
Scalar Optimality ◽  
Derivatives Of

Abstract In our paper we will continue the comparison which was started by Vsevolod I. Ivanov [Nonlinear Analysis 125 (2015), 270–289], where he compared scalar optimality conditions stated in terms of Hadamard derivatives for arbitrary functions and those which was stated for ℓ-stable functions in terms of Dini derivatives. We will study the vector optimization problem and we show that also in this case the optimality condition stated in terms of Hadamard derivatives is more advantageous.

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