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Item Método do gradiente para funções convexas generalizadas(Universidade Federal de Goiás, 2009-12-16) COUTO, Kelvin Rodrigues; FERREIRA, Orizon Pereira; lattes.cnpq.br/0201145506453251The Convergence theory of gradient method and gradient projection method, for minimization of continuously differentiable generalized convex functions, that is, pseudoconvex functions and quasiconvex functions is studied in this work. We shall see that under certain conditions the gradient method, as well as gradient projection method, generate a convergent sequence and the limit point is a minimizing, whenever the function has minimizing and is pseudoconvex functions. If the objective function is quasiconvex then the generated sequence converges to a stationary point whenever that point exists.Item Método de Descida para problemas de otimização multiobjetivo(Universidade Federal de Goiás, 2010-04-30) JESUS, Lays Grazielle Cardoso Silva de; PEREZ, Luis Román Lucambio; http://lattes.cnpq.br/6532280983965503In this work, we study the descent of methods for problem of optimization multiobjective which we introduce an order of relation induced by an closed convex cone.We study as it wiel calculate an descent of direction and we prove that every accumalation point of the sequence generated by the descent of methods with search of Armijo is weakly efficient.Item Método Subgradiente Condicional com Sequência Ergódica(Universidade Federal de Goiás, 2011-02-18) SILVA, Jose Carlos Rubianes; MELO, Jefferson Divino Gonçalves de; http://lattes.cnpq.br/8296171010616435In this dissertation we consider a primal convex optimization problem and we study variants of subgradient method applied to the dual problem obtained via a Lagrangian function. We analyze the conditional subgradient method developed by Larsson et al, which is a variant of the usual subgradient method. In this variant, the subgradients are conditioned to a constraint set, more specifically, the behavior of the objective function outside of the constraint set is not taken into account. One motivation for studying such methods is primarily its simplicity, in particular, these methods are widely used in large-scale problems. The subgradient method, when applied to a dual problem, is relatively effective to obtain a good approximation of a dual solution and the optimal value, but it is not efficient to obtain primal solutions. We study a strategy to obtain good approximations of primal solutions via conditional subgradient method, under suitable additional computational costs. This strategy consists of constructing an ergodic sequence of solutions of the Lagrangian subproblems.We show that the limit points of this ergodic sequence are primal solutions. We consider different step sizes rule, in particular, following the ideas of Nedic and Ozdaglar, using the constant step size rule, we present estimates of the ergodic sequence and primal solutions and / or the feasible set.