Invited Session Fri.3.MA 313

Friday, 15:15 - 16:45 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Contraction methods for separable convex optimization in the frame of VIs

 

Chair: Bingsheng He

 

 

Friday, 15:15 - 15:40 h, Room: MA 313, Talk 1

Guoyong Gu
Customized proximal point algorithms: A unified approach

Coauthors: Bingsheng He, Xiaoming Yuan

 

Abstract:
This talk takes a unified look at the customized applications of proximal point algorithms (PPA) to two classes of problems, namely, the linearly constrained convex problem with a generic or separable objective function and a saddle-point problem. We model these two classes of problems as mixed variational inequalities, and show how PPA with customized proximal parameters can yield favorable algorithms, which are able to exploit the structure of the models. Our customized PPA revisit turns out to be a unified approach in designing a number of efficient algorithms, which are competitive with, or even more efficient than some benchmark methods in the existing literature such as the augmented Lagrangian method, the alternating direction method and a class of primal-dual methods, etc. From the PPA perspective, the global convergence and the O(1/t) convergence rate are established in a uniform way.

 

 

Friday, 15:45 - 16:10 h, Room: MA 313, Talk 2

Min Tao
A slightly changed alternating direction method of multipliers for separable convex programming

Coauthors: Sheng Bing He, Ming Xiao Yuan

 

Abstract:
The classical alternating direction method of multiliers (ADMM) has
been well studied in the context of linearly constrained convex
programming and variational inequalities where the involved operator
is formed as the sum of two individual functions without crossed
variables. Recently, ADMM has found many novel applications in
diversified areas such as image processing and statistics. However,
it is still not clear whether ADMM can be extended to the case where
the operator is the sum of more than two individual functions. In
this paper, we present a ADMM with minor change for solving the
linearly constrained separable convex optimization whose involved
operator is separable into three individual functions. The
O(1/t) convergence rate of the proposed methods is
demonstrated.

 

 

Friday, 16:15 - 16:40 h, Room: MA 313, Talk 3

Xingju Cai
ADM based customized PPA for separable convex programming

Coauthors: Guoyong Gu, Bingsheng He, Xiaoming Yuan

 

Abstract:
The ADM is classical for solving a linearly constrained separable convex programming problem, and it is well known that ADM is essentially the application of a concrete form of the PPA to the corresponding dual problem. This paper shows that an efficient method competitive to ADM can be easily derived by applying PPA directly to the primal problem. More specifically, if the proximal parameters are chosen judiciously according to the separable structure of the primal problem, the resulting customized PPA takes a similar decomposition algorithmic framework as that of ADM. The customized PPA and ADM are equally effective to exploit the separable structure of the primal problem, equally efficient in numerical senses and equally easy to implement. Moreover, the customized PPA is ready to be accelerated by an over-relaxation step, yielding a relaxed customized PPA for the primal problem. We verify numerically the competitive efficiency of the customized PPA to ADM, and the effectiveness of the over-relaxation step. Furthermore, we provide a simple proof for the O(1/t) convergence rate of the relaxed customized PPA.

 

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