A generalization of a theorem of Arrow, Barankin and Blackwell to a nonconvex case
- Authors: Kasimbeyli, Nergiz , Kasimbeyli, Refail , Mammadov, Musa
- Date: 2016
- Type: Text , Journal article
- Relation: Optimization Vol. 65, no. 5 (May 2016), p. 937-945
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- Description: The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a partially ordered reflexive Banach space.
A sharp augmented Lagrangian-based method in constrained non-convex optimization
- Authors: Bagirov, Adil , Ozturk, Gurkan , Kasimbeyli, Refail
- Date: 2019
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 34, no. 3 (2019), p. 462-488
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- Description: In this paper, a novel sharp Augmented Lagrangian-based global optimization method is developed for solving constrained non-convex optimization problems. The algorithm consists of outer and inner loops. At each inner iteration, the discrete gradient method is applied to minimize the sharp augmented Lagrangian function. Depending on the solution found the algorithm stops or updates the dual variables in the inner loop, or updates the upper or lower bounds by going to the outer loop. The convergence results for the proposed method are presented. The performance of the method is demonstrated using a wide range of nonlinear smooth and non-smooth constrained optimization test problems from the literature.