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Adaptive trust region scheme for multi-objective optimization problem using Geršgorin circle theorem

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Abstract

In this article, a trust region algorithm is proposed to solve multi-objective optimization problem. A sequence of points is generated using Geršgorin Circle theorem with a modified secant equation. This sequence converges to a critical point of the problem. At every iteration, a common positive definite matrix is considered to take care of all the objective functions simultaneously and the radius of the trust region is obtained in an explicit form. Global convergence of the method is established with numerical support using a set of test problems.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, India

    Nantu Kumar Bisui & Geetanjali Panda

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  1. Nantu Kumar Bisui
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  2. Geetanjali Panda
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Correspondence to Geetanjali Panda.

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Bisui, N.K., Panda, G. Adaptive trust region scheme for multi-objective optimization problem using Geršgorin circle theorem. J. Appl. Math. Comput. 68, 2151–2172 (2022). https://doi.org/10.1007/s12190-021-01602-0

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  • DOI: https://doi.org/10.1007/s12190-021-01602-0

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