319. Complex geometrical test for optimality conditions in Interval Branch and Bound method
Invited abstract in session TB-7: Global optimization I, stream Global optimization.
Thursday, 10:05 - 11:20Room: M:I
Authors (first author is the speaker)
| 1. | Boglárka G.-Tóth
|
| Department of Computational Optimization, University of Szeged | |
| 2. | Mihály Gencsi
|
| Computational Optimization, University of Szeged |
Abstract
This study focuses on solving constrained nonlinear programming problems. The Interval Branch and Bound (IBB) method is the most widely used approach for obtaining rigorous solutions. However, few IBB implementations utilize the Karush-Kuhn-Tucker or Fritz-John optimality conditions to eliminate non-optimal boxes. The Fritz-John optimality condition involves solving an interval-valued system of equations. When solving these equations, we sometimes cannot reduce the size of the box due to overestimation of the gradient boxes.
This study considers the optimality conditions from a geometric perspective. A new, more complex geometrical optimality test is introduced to precede the Fritz-John optimality condition. The goal is to speed up the IBB method and eliminate unnecessary computations.
The test easily ensures that there is no local optimum in the box, or that we cannot reduce the size of the box by solving the optimality condition system because of the overestimation of the gradient boxes. We will describe the geometric test and its usefulness, as well as present experimental results demonstrating the effectiveness of the complex geometrical test.
Keywords
- Global optimization
Status: accepted
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