Convergence of the projected gradient method for quasiconvex multiobjective optimization

• Published in: Nonlinear analysis Vol. 74; no. 16; pp. 5268 - 5273
• Main Authors: Bello Cruz, J.Y., Lucambio Pérez, L.R., Melo, J.G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.11.2011; Elsevier
• Subjects: Algorithms; Armijo-type search; Calculus of variations and optimal control; Convergence; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Multiobjective optimization; Nonlinearity; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Optimization; Pareto optimality; Projected gradient methods; Quasiconvex multiobjective functions; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; 90C30; Multiobjective optimization; Pareto-optimality; 90C29; Armijo-type search; Projected gradient methods; Quasiconvex multiobjective functions; Nonlinear analysis; Optimization method; Algorithm; Weak convergence; Problem solving; Mathematical model; Gradient method
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2011.04.067

We consider the projected gradient method for solving the problem of finding a Pareto optimum of a quasiconvex multiobjective function. We show convergence of the sequence generated by the algorithm to a stationary point. Furthermore, when the components of the multiobjective function are pseudoconvex, we obtain that the generated sequence converges to a weakly efficient solution.