QA271 : Some Iterative Methods For Multiobjective Optimization Problems
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2015
Authors:
Abstarct: In this thesis, we first introduce the basic concepts and preliminaries. Then, we express the concepts of the efficiency and weak efficiency for multiobjective optimization problem. We deal to solve multiobjective optimization problem by applying iterative methods. An iterative method is a computational process that generates a sequence and we expect that under reasonable conditions converges to the efficient solution of the problem.
From the iterative methods for multiobjective optimization problem, we discuss, the Newton method and the quasi-Newton methods.
Following, we express the Newton algorithm for solving convex multiobjective optimization problem that requires precise calculation of the Hessian matrix for each objective function. In the case that calculation of the Hussein be difficult, quasi-Newton methods are introduced and are discussed.
These methods calculate the Hessian approximate instead of the exact Hessian and help us to improve the solving process.
In cases where the problem is nonconvex, a modified quasi-Newton algorithm is suggested.
In this case, by calculating an approximate matrix, nonconvex multiobjective problems are solved.
Finally, a quasi-Newton method for solving nonsmooth multiobjective problem is introduced.
Keywords:
#Multiobjective optimization #Efficient solution #Weakly efficient solution #Critical point #Convex function Link
Keeping place: Central Library of Shahrood University
Visitor:
Keeping place: Central Library of Shahrood University
Visitor: