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Quasi-Newton Method for Set Optimization Problems with Set-Valued Mapping Given by Finitely Many Vector-Valued Functions by Ghosh, Debdas; Anshika; Yao, Jen-Chih; Zhao, Xiaopeng is a scholarly article available to read on EtoBox.

What is Quasi-Newton Method for Set Optimization Problems with Set-Valued Mapping Given by Finitely Many Vector-Valued Functions about?

In this article, we propose a quasi-Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The set-valued objective mapping under consideration is given by a finite number of vector-valued functions that are twice continuously differentiable. To find the necessary optimality condition for weak minimal points with the help of the proposed quasi-Newton method, we use the concept of partition and formulate a family of vector optimization problems. The evaluation of necessary optimality condition for finding the weakly minimal points involves the computation of the approximate Hessian of every objective function, which is done by a quasi-Newton scheme for vector optimization problems. In the proposed quasi-Newton method, we derive a sequence of iterative points that exhibits convergence to a point which satisfies the derived necessary optimality condition for weakly minimal points. After that, we find a descent direction for a suitably chosen vector optimization problem from this family of vector optimization problems and update from the current iterate to the next iterate. The proposed quasi-Newton method

Author

Ghosh, Debdas; Anshika; Yao, Jen-Chih; Zhao, Xiaopeng

Published

2024

Language

EN