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This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical… (More)

- Hellena Christina Fernandes Apolinário, Erik A. Papa Quiroz, P. Roberto Oliveira
- J. Global Optimization
- 2016

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… (More)

- Erik A. Papa Quiroz, L. Mallma Ramirez, P. Roberto Oliveira
- European Journal of Operational Research
- 2015

In this paper we propose an inexact proximal point method to solve constrained minimization problems with locally Lipschitz quasiconvex objective functions. Assuming that the function is also bounded from below, lower semicontinuous and using proximal distances, we show that the sequence generated for the method converges to a stationary point of the… (More)

- Erik A. Papa Quiroz, P. Roberto Oliveira
- European Journal of Operational Research
- 2012

- N. Baygorrea, Erik A. Papa Quiroz
- 2015

In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand… (More)

- Erik A. Papa Quiroz
- J. Global Optimization
- 2013

This paper extends the full convergence of the proximal point method with Riemannian, Semi-Bregman and Bregman distances to solve minimization problems on Hadamard manifolds. For the unconstrained problem, under the assumptions that the optimal set is nonempty and the objective function is continuous and either quasiconvex or satisfies a generalized… (More)

- Erik A. Papa Quiroz, P. Roberto Oliveira
- RAIRO - Operations Research
- 2006

We introduce a new barrier function to solve a class of Semidefinite Optimization Problems (SOP) with bounded variables. That class is motivated by some (SOP) as the minimization of the sum of the first few eigenvalues of symmetric matrices and graph partitioning problems. We study the primal-dual central path defined by the new barrier and we show that… (More)

This paper analyze the convergence rate of a proximal algorithm called Proximal Multiplier Algorithm with Proximal Distances (PMAPD), proposed by us in [20], to solve convex minimization problems with separable structure. We prove that, under mild assumptions, its primal-dual sequences converge linearly to the optimal solution for a class of proximal… (More)

In this paper we propose an inexact proximal point method to solve equilibrium problem using proximal distances and the diagonal subdifferential. Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction, we prove that the sequence generated for the method converges to a solution point of the problem.