scholarly journals Min–sup-type zero duality gap properties for DC composite optimization problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Li Ping Tian ◽  
Dong Hui Fang
Keyword(s):  
Optimization Problem ◽  
Duality Gap ◽  
Zero Duality Gap ◽  
Composite Optimization

scholarly journals Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem

2019 ◽  
Vol 10 ◽  
pp. A10
Author(s):  
Mansur Hassan ◽  
Adam Baharum
Keyword(s):  
Penalty Function ◽  
Optimization Problem ◽  
Duality Gap ◽  
Penalty Function Method ◽  
Constrained Optimization Problem ◽  
Zero Duality Gap ◽  
Invex Functions ◽  
Lagrangian Dual ◽  
Nonlinear Mathematical Programming ◽  
Mathematical Programming Problems

In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.

Zero duality gap conditions via abstract convexity∗

Optimization ◽  
2021 ◽  
pp. 1-37
Author(s):  
Hoa T. Bui ◽  
Regina S. Burachik ◽  
Alexander Y. Kruger ◽  
David T. Yost
Keyword(s):  
Duality Gap ◽  
Abstract Convexity ◽  
Zero Duality Gap

Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap

2017 ◽  
Vol 69 (4) ◽  
pp. 823-845 ◽  
Author(s):  
Fabián Flores-Bazán ◽  
William Echegaray ◽  
Fernando Flores-Bazán ◽  
Eladio Ocaña
Keyword(s):  
Nonconvex Optimization ◽  
Strong Duality ◽  
Duality Gap ◽  
Zero Duality Gap

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.

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