3,153 research outputs found
A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem
The problem (LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for (LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems.This research was partially supported by MICINN of Spain, Grant MTM2014-59179-C2-1-P and Sistema Nacional de Investigadores, Mexico
A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem
The problem (LFP) of finding a feasible solution to a given linear
semi-infinite system arises in different contexts. This paper provides
an empirical comparative study of relaxation algorithms for (LFP).
In this study we consider, together with the classical algorithm, imple-
mented with different values of the fixed parameter (the step size), a
new relaxation algorithm with random parameter which outperforms
the classical one in most test problems whatever fixed parameter is
taken. This new algorithm converges geometrically to a feasible so-
lution under mild conditions. The relaxation algorithms under com-
parison have been implemented using the Extended Cutting Angle
Method (ECAM) for solving the global optimization subproblems.Peer ReviewedPreprin
Discrete-Continuous ADMM for Transductive Inference in Higher-Order MRFs
This paper introduces a novel algorithm for transductive inference in
higher-order MRFs, where the unary energies are parameterized by a variable
classifier. The considered task is posed as a joint optimization problem in the
continuous classifier parameters and the discrete label variables. In contrast
to prior approaches such as convex relaxations, we propose an advantageous
decoupling of the objective function into discrete and continuous subproblems
and a novel, efficient optimization method related to ADMM. This approach
preserves integrality of the discrete label variables and guarantees global
convergence to a critical point. We demonstrate the advantages of our approach
in several experiments including video object segmentation on the DAVIS data
set and interactive image segmentation
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