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A conjugate directions-type procedure for quadratic multiobjective optimization

Ellen H. Fukuda(ellen***at***i.kyoto-u.ac.jp)
L. M. Graņa Drummond(bolsigeno***at***gmail.com)
Ariane M. Masuda(amasuda***at***citytech.cuny.edu)

Abstract: We propose an extension of the real-valued conjugate directions method for unconstrained quadratic multiobjective problems. As in the single-valued counterpart, the procedure requires a set of directions that are simultaneously conjugate with respect to the positive definite matrices of all quadratic objective components. Likewise, the multicriteria version computes the steplength by means of the unconstrained minimization of a single-variable strongly convex function at each iteration. When it is implemented with a weakly-increasing (strongly-increasing) auxiliary function, the scheme produces weak Pareto (Pareto) optima in finitely many iterations.

Keywords: Multiobjective optimization; weak Pareto optimality; Pareto optimality; conjugate directions method

Category 1: Other Topics (Multi-Criteria Optimization )


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Entry Submitted: 07/28/2020
Entry Accepted: 08/01/2020
Entry Last Modified: 07/28/2020

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