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808. A New Derivative-free Method Using an Improved Under-determined Quadratic Interpolation Model

Invited abstract in session WC-42: Nonlinear optimization algorithms and applications, stream Variational Analysis and Continuous Optimization.

Wednesday, 12:30-14:00
Room: 98 (building: 306)

Authors (first author is the speaker)

1. Ya-xiang Yuan
Institute of Computational Mathematics and Sci./Eng. Computing, AMSS, Chinese Academy of Sciences

Abstract

In this talk, we give a new derivative-free method by introducing an improved under-determined quadratic interpolation model. We analyze the least norm type under-determined quadratic interpolation model proposed by Conn and Toint from the perspective of the property of trust-region iteration. We found the Karush-Kuhn-Tucker multiplier's non-determinacy when constructing a quadratic model considering the trust-region iteration in the case where the current iteration point is on the boundary of the trust region. The lack of the quadratic model's uniqueness caused by the Karush–Kuhn–Tucker multiplier's non-determinacy leads us to propose a new model by selectively treating the last obtained under-determined quadratic model as a quadratic model or a linear one. We propose the theoretical motivation, computational details, and the quadratic model's formula derived from the Karush-Kuhn-Tucker conditions. The formula is implementation-friendly for the existing model-based derivative-free methods. The numerical results with released codes support the advantages of our quadratic model in the derivative-free optimization methods. To the best of our knowledge, this is the first work considering the
property of trust-region iteration and the model's optimality when constructing the under-determined quadratic model for derivative-free trust-region methods.

Keywords

Status: accepted

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