A conjugate directions-type procedure for quadratic multiobjective optimization. (1st February 2022)

• Record Type: Journal Article
• Authors: Fukuda, Ellen H.; Graña Drummond, L. M.; Masuda, Ariane M.
• Is Part Of: Optimization. Volume 71:Number 2(2022)
• Page Start: 419
• Page End: 437
• Publication Date: 2022-02-01
• Subjects: Multiobjective optimization -- weak Pareto optimality -- Pareto optimality -- conjugate directions method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1914034
• Languages: English
• ISSNs: 0233-1934

Abstract

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.