Seminários de Otimização 2010-1
Os seminários do Grupo de Otimização do IME, UFG, no primeiro semestre 2010, acontecerá nas quarta-feiras as 16-17 horas. Local: FACOMB, sala 24.
| Palestrante | Título | ||
|---|---|---|---|
| 10 |
Março | Luis Roman Lucambio Pérez | A variant of the projected gradient method for quasi-convex optimization problems with an efficient search strategy I. |
| Resumo: We present a variant of projected gradient method for solving uncon- strained minimization problem with a quasi-convex objective function. We pro- posed an appropriate stepsize in each iteration through the Armijo search along the feasible direction. Differently from other similar schemes, we perform only one projection onto the feasible set in each iteration, rather than one projection for each tentative step during the search, which represents a considerable saving when the projection is computationally expensive. |
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| 17 | Luis Roman Lucambio Pérez | A variant of the projected gradient method for quasi-convex optimization problems with an efficient search strategy I. | |
| Resumo: We present a variant of projected gradient method for solving uncon- strained minimization problem with a quasi-convex objective function. We pro- posed an appropriate stepsize in each iteration through the Armijo search along the feasible direction. Differently from other similar schemes, we perform only one projection onto the feasible set in each iteration, rather than one projection for each tentative step during the search, which represents a considerable saving when the projection is computationally expensive. |
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| 24 | José Yunier Bello Cruz | Full convergence of an approximate projections method for nonsmooth variational inequalities. | |
| Resumo: We introduce a fully explicit method for solving nonsmooth monotone variational inequalities in Hilbert spaces, where orthogonal projections onto feasible set are replaced by projections onto suitable hyperplanes. We prove weak conver- gence of the whole generated sequence to a solution of the problem, under the only assumptions of maximal monotonicity of the operator and existence of solutions. |
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| 31 | Geci José Pereira da Silva | ||
| 07 | Abril | José Yunier Bello Cruz | An Explicit Algorithm for Nonsmooth Monotone Variational Inequalities in Hilbert Spaces. |
| Resumo: We introduce a fully explicit method for solving nonsmooth monotone variational inequalities in Hilbert spaces, where orthogonal projections onto feasible set are replaced by projections onto suitable hyperplanes. We prove weak conver- gence of the whole generated sequence to a solution of the problem, under the only assumptions of maximal monotonicity of the operator and existence of solutions. |
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| 14 | Laiz Grazielle Cardoso Silva | ||
| 21 | (Feriado) | ||
| 28 | Glaydston de Carvalho Bento | Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemania Manifolds. | |
| Resumo: We present a steepest descent method with Armijo's rule for multicriteria optimization in a Riemannian context. The well definedness of the sequence generated by the method is guaranteed. Under mild assumptions on the multicriteria function, it is proved that each accumulation point (if one exists) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming quasi-convexity of the multicriteria function and non-negative curvature of the Riemannian manifold, full convergence of the sequence to a Pareto critical is proved. | |||
| 05 | Maio | Glaydston de Carvalho Bento | Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemania Manifolds. |
| 12 | Geci José Pereira da Silva | ||
| 19 | Jefferson G. Melo | Método Subgradiente Modificado e Lagrangiana Sharp | |
| Discutiremos algumas propriedades de um método subgradiente modificado aplicado a um problema dual construído via Lagrangiana Sharp. Não supomos hipóteses de convexidade ou diferenciabilidade do problema primal. Mostraremos que o método é de subida e apresentaremos modificações que garantem convergência da sequência primal. | |||
| 26 | Jefferson G. Melo | Método Subgradiente Modificado e Lagrangiana Sharp | |
| 02 | Junho | Max Leandro Nobre Gonçalves | Local Convergence Analysis of Inexact Gauss-Newton like Methods under Majorant Conditions |
| We present a local convergence analysis of inexact Gauss-Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, we obtain that the method is well-defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the least square problem. It also allow us to obtain an estimate of convergence ball for inexact Gauss-Newton like methods and some important special cases. | |||
| 09 | Ole Peter Smith | Implementation of an Improved Projected Gradient Algorithm | |
| In this seminar, we introduce an improved projected gradient algorithm by Bello Cruz et al., along with it's numerical implementation. Some preliminary numerical experiments are shown, along with (in the 2D case) it's graphical visualization. |
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| 16 | Carlos Rubianes Silva | ||
| 23 | Kelvin Rodrigues Couto | Generalized invex monotone functions | |
| We introduce generalized invex monotone functions, that are defined as an extension of monotone functions. A series of sufficient and necessary are also given that relate the generalized invexity of the function z with the generalized invex monotonicity of its gradient function. |
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| 30 | Rogerio Quiroz Chaves | ||
Fonte: Coordenação do grupo de otimização