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Published in:
2016 | OriginalPaper | Chapter
5. Constrained Optimization
Authors : Mongi A. Abidi, Andrei V. Gribok, Joonki Paik
Published in: Optimization Techniques in Computer Vision
Publisher: Springer International Publishing
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Abstract
In most practical image processing and computer vision problems involving optimization, the solutions do not span the entire range of real values. This resulting bounding property is often imposed upon the solution process in the form of constraints placed upon system parameters. Optimization problems with constraints are generally referred to as constrained optimization problems.
The basic idea of solving most constrained optimization problems is to determine the solution that satisfies the stated performance index, subject to the given constraints. In this chapter, proper methods of finding the solutions to constrained optimization problems, according to the characteristics of various types of constraints, are discussed.
If the solution and its local perturbation do not violate the given constraints, we consider the problem as being unconstrained. Therefore, the important issue of constrained optimization is analyzing the local behavior of the solution on or near the boundary of constraints.
This chapter includes three sections. The first section describes the constrained optimization problem and defines the terminology commonly used with this problem, both in the literature and in this chapter. The second and the third sections describe optimality conditions and the corresponding optimization methods with linear and nonlinear constraints, respectively.