The modified subgradient algorithm based on feasible values
- Authors: Kasimbeyli, Refail , Ustun, Ozden , Rubinov, Alex
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 535-560
- Full Text: false
- Reviewed:
- Description: In this article, we continue to study the modified subgradient (MSG) algorithm previously suggested by Gasimov for solving the sharp augmented Lagrangian dual problems. The most important features of this algorithm are those that guarantees a global optimum for a wide class of non-convex optimization problems, generates a strictly increasing sequence of dual values, a property which is not shared by the other subgradient methods and guarantees convergence. The main drawbacks of MSG algorithm, which are typical for many subgradient algorithms, are those that uses an unconstrained global minimum of the augmented Lagrangian function and requires knowing an approximate upper bound of the initial problem to update stepsize parameters. In this study we introduce a new algorithm based on the so-called feasible values and give convergence theorems. The new algorithm does not require to know the optimal value initially and seeks it iteratively beginning with an arbitrary number. It is not necessary to find a global minimum of the augmented Lagrangian for updating the stepsize parameters in the new algorithm. A collection of test problems are used to demonstrate the performance of the new algorithm. © 2009 Taylor & Francis.
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
- Full Text: false
- Reviewed:
- 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.