Entropy-like proximal methods in convex programming
Mathematics of Operations Research
Dominating sets for convex functions with some applications
Journal of Optimization Theory and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Explicit gradient information in multiobjective optimization
Operations Research Letters
Discontinuous Galerkin unsteady discrete adjoint method for real-time efficient tsunami simulations
Journal of Computational Physics
Quasi-Newton's method for multiobjective optimization
Journal of Computational and Applied Mathematics
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In this work we propose a Cauchy-like method for solving smooth unconstrained vector optimization problems. When the partial order under consideration is the one induced by the nonnegative orthant, we regain the steepest descent method for multicriteria optimization recently proposed by Fliege and Svaiter. We prove that every accumulation point of the generated sequence satisfies a certain first-order necessary condition for optimality, which extends to the vector case the well known "gradient equal zero" condition for real-valued minimization. Finally, under some reasonable additional hypotheses, we prove (global) convergence to a weak unconstrained minimizer.As a by-product, we show that the problem of finding a weak constrained minimizer can be viewed as a particular case of the so-called Abstract Equilibrium problem.