## Seminar 2017.2

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Organized by  Max L.N. Gonçalves
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------

The seminars in this semester will be held in the Lecture Room of IME/UFG, unless otherwise stated. All interested are very welcome to attend.

------------------------------------------------------------------------------------------------------------------------------------------

Title: Quasi-Newton methods for convex constrained nonlinear systems.

Speaker: Fabricia R. Oliveira (Ph.D. student-IME/UFG)

Abstract: In this talk, we will present a new linesearch Quasi-Newton methods. These methods are based on a proper use of the projection map onto the constraint set and on a derivative-free and nonmonotone linesearch strategy.

Data: 22/08/2017
Hora: 10:00 hrs

------------------------------------------------------------------------------------------------------------------------------------------

Title: Pointwise and ergodic convergence rates of a variable metric proximal ADMM

Speaker: Max L. N. Gonçalves (Professor-IME/UFG)

Abstract:  In this talk, we discuss pointwise and ergodic convergence rates for a variable metric proximal alternating direction method of multiplicas (VM-PADMM) for solving linearly constrained convex optimization problems. The VM-PADMM can be seen as a class of ADMM variants, allowing the use of degenerate metrics (defined by noninvertible linear operators). We first propose and study nonasymptotic convergence rates of a variable metric hybrid proximal extragradient (VM-HPE) framework for solving monotone inclusions. Then, the convergence rates for the VM-PADMM are obtained essentially by showing that it falls within the latter framework.

Data: 29/08/2017
Hora: 10:00 hrs

------------------------------------------------------------------------------------------------------------------------------------------

Title: The Newton’s method for vector fields on Riemannian Manifolds

Speaker: Fabiana R. Oliveira (Ph.D. student-IME/UFG)

Abstract: In this seminar we will present the Newton's method for finding a singularity of a vector field defined on complete Riemannian manifolds, and discuss some ideas about its convergence analysis.

Data: 05/09/2017
Hora: 10:00 hrs

---------------------------------------------------------------

Title: Optimization Methods in the Riemannian Context.

Speaker: Mauricio S. Louzeiro (Ph.D. student-IME/UFG)

Abstract: In this talk, we will present well-known results related to the convergence of convex programming methods, with the aim of minimizing a convex function defined on a complete Riemannian manifold. In addition, we will comment on the importance of the Toponogov Theorem in the convergence analysis of some methods.

Data: 12/09/2017
Hora: 10:00 hrs

------------------------------------------------------------------------------------------------------------------------------------------

Title: A symmetric version of the generalized alternating direction method of multipliers for
two-block separable convex programming

Speaker: Vando A. Adona (Ph.D. student-IME/UFG)

Abstract: In this talk, we will analyze the iteration-complexity of a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the advantages of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor of the generalized ADMM. More specifically, we will show that the symmetric ADMM is an instance of a hybrid proximal extragradient framework.

Reference:
[1] Jing Liu, Yongrui Duan and Min Sun. A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming. Journal of Inequalities and Applications, (1) 2017:129, 2017.

Data: 26/09/2017
Hora: 10:00 hrs

------------------------------------------------------

Title: A regularized proximal point method and its iteration complexity

Speaker: Jefferson D. G. Melo (Professor-IME/UFG)

Abstract: In this talk, we present a regularized version of the proximal point method which has pointwise iteration complexity O(1/p)log(1/p), improving considerably the O(1/p^2) of the standard proximal point method.

Data: 03/10/2017
Hora: 10:00 hrs

-----------------------------

Title: On the splitting optimization problem with enlargement

Speaker: Reinier D. Millan (Professor do IFG)

Abstract: Given a Hilbert space $\HH$ and a convex functions $f:\dom f\subseteq \HH \rightarrow \R$ and $g:\dom g\subseteq \HH \rightarrow \R$, the Splitting Constrained Optimization Problem ({\emph SCOP}) consist in:

\min_{x\in C} \, f(x) + g(x),

where $C\subseteq \HH$ is a convex and closed set. In this paper, we present two inexact algorithms for solving SCOP. Due to the complexity,in some cases, of computing the proximal operator or the resolvent operator, is
imperative to consider relaxed procedures to compute this operator. Our scheme follows
the ideas of the $\epsilon-$subdifferential and the inexact proximal point method. The convergence analysis for
different stepsizes are presented and some numerical expereminets show the behaviour of our algorithm.

Data: 19/10/2017
Hora: 08:00 hrs

-------------------------------------------------------------------------------------------------------

Title: On a Gauss-Newton method for solving bound-constrained underdetermined nonlinear systems

Speaker: Fabrícia R. Oliveira (Ph.D. student-IME/UFG)

Abstract: In this talk, we will present a method for solving bound-constrained underdetermined nonlinear systems.We also will discuss results on the  global convergence of the method.

Data: 26/10/2017
Hora: 08:00 hrs

-------------------------------------------------------------------------------------------------------

Title: Proximal alternating direction method of multipliers with larger step size for convex programming with separable structure

Speaker: Vando A. Adona (Ph.D. student-IME/UFG)

Abstract: In this talk, we will present pointwise and ergodic convergence rates for the proximal Alternating Direction Method of Multipliers with larger step size. This version proximal ADMM extends the feasible set, where the update step is chosen, to the interval (0, 2). Some numerical experiments  are given to demonstrate the effciency and the performance of the method.

Data: 09/11/2017
Hora: 08:00 hrs

-----------------------------------------------------

Title: Variante Konnov do Algoritmo HPE

Speaker: Paulo César da Silva Júnior (Ph.D. student-IME/UFG)

Data: 16/11/2017
Hora: 08:00 hrs

--------------------------

Title: Método do ponto proximal para funções localmente Lipschitz em otimização multiobjectivo

Speaker: Lucas Vidal Meireles (Ph.D. student-IME/UFG)

Abstract: Nesta exposição, apresentaremos um método do ponto proximal para programação multiobjectivo em que a função vetorial é localmente Lipschitz. Faremos a análise de convergência, provando que todo ponto de acumulação da sequência gerada por este algoritmo, caso exista, é Pareto crítico da função objetivo. Além disso, sob hipótese de convexidade garantiremos convergência a Pareto fraco.

Data: 23/11/2017
Hora: 08:00 hrs

------------------- ----------

Title: Functions defined in Riemannian Manifolds - examples

Speaker: Maurício S. Louzeiro (Ph.D. student-IME/UFG)

Abstract: In this talk will be presented special examples of functions defined in Riemannian Manifolds with curvature 0
and with curvature bounded lower by a negative constants. In particular, we will show that by introducing a suitable
Riemannian metric, a Euclidean optimization problem having objective function non-convex with gradient non-Lipschitz
can be transformed into Riemanian optimization problem with objective convex function with gradient Lipschitz.

Data: 30/11/2017
Hora: 14:00 hrs

-------------

Title: Iteration-complexity of a Jacobi-type non-Euclidean ADMM for
multi-block linearly constrained non-convex programs

Speaker: Renato D.C. Monteiro (ISyE  Georgia Institute of Technology  Atlanta-GA, USA).

Abstract: This talk presents the iteration-complexity of a Jacobi-type non-Euclidean proximal al-
ternating direction method of multipliers (ADMM) variant for solving (i.e., finding
approximate stationary points of) multi-block linearly constrained non-convex programs.
Since the subproblems of this ADMM variant can be solved in parallel, the variant
has great potential to solve large scale multi-block linearly constrained non-convex programming
instances. Also, our analysis allows the Lagrange multiplier to be updated with a relaxation
parameter in the interval (0, 2), and hence extends other previous works which only allow the
parameter to chosen in the interval (0,1.618).

Data: 07/12/2017
Hora: 13:00 hrs

------------------

Presentation Schedule:

14/12/2017-Fabiana R. Oliveira (Ph.D. student-IME/UFG)

21/12/2017-Lucas Vidal Meireles (Ph.D. student-IME/UFG)

Coordinator schedule:

Orizon P. Ferreira (2018/1)

Reinier Diaz Millan (2018/2)

Luis Roman (2019/1)

Leandro F. Prudente (2019/2)

Glaydston C. Bento (2020/1)

Jefferson D. G. Melo (2020/2)