We introduce a proximal algorithm using quasidistances for multiobjective minimization problems with quasiconvex functions defined in arbitrary Riemannian manifolds. The reason of using quasidistances instead of the c...
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We introduce a proximal algorithm using quasidistances for multiobjective minimization problems with quasiconvex functions defined in arbitrary Riemannian manifolds. The reason of using quasidistances instead of the classical Riemannian distance comes from the applications in economy, computer science and behavioral sciences, where the quasidistances represent a non symmetric measure. Under some appropriate assumptions on the problem and using tools of Riemannian geometry we prove that accumulation points of the sequence generated by the algorithm satisfy the critical condition of Pareto-Clarke. If the functions are convex then these points are Pareto efficient solutions.
In this paper we present an inexact scalarization proximal point algorithm to solve unconstrained multiobjective minimization problems where the objective functions are quasiconvex and locally Lipschitz. Under some na...
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In this paper we present an inexact scalarization proximal point algorithm to solve unconstrained multiobjective minimization problems where the objective functions are quasiconvex and locally Lipschitz. Under some natural assumptions on the problem, we prove that the sequence generated by the algorithm is well defined and converges. Then providing two error criteria we obtain two versions of the algorithm and it is proved that each sequence converges to a Pareto-Clarke critical point of the problem;furthermore, it is also proved that assuming an extra condition, the convergence rate of one of these versions is linear when the regularization parameters are bounded and superlinear when these parameters converge to zero.
In this paper, we propose a linear scalarization proximal point algorithm for solving lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and, using the condition that...
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In this paper, we propose a linear scalarization proximal point algorithm for solving lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and, using the condition that the proximal parameters are bounded, we prove the convergence of the sequence generated by the algorithm and, when the objective functions are continuous, we prove the convergence to a generalized critical point of the problem. Furthermore, for the continuously differentiable case we introduce an inexact algorithm, which converges to a Pareto critical point.
In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, ...
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In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for nonconvex case, of the inexact proximal method for multiobjective convex minimization problems studied by Bonnel et al. (SIAM J Optim 15(4):953-970, 2005).
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