A class of group symmetric Semi-Definite Program (SDP) is introduced by using the framework of group representation theory. It is proved that the central path and several search directions of primal-dual interior-point methods are group symmetric. Preservation of group symmetry along the search direction theoretically guarantees that the numerically obtained optimal solution is group symmetric....

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima, Megiddo and Mizuno (A primal-dual infeasibleinterior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an a...

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remain...

We explore a symmetry-based reformulation technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by over 30 times. Our offline approach decomposes grid maps into a set of empty rectangles, removing from each all interior nodes and possibly some from along the perimeter. We then add macro-edges between selected pairs of remaining perimeter nodes to facilitate prova...

Sparse covariance selection problems can be formulated as log-determinant (log-det ) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized ...

This article introduces two swarm intelligent algorithms, a group search optimizer (GSO) and an artificial fish swarm algorithm (AFSA). A single intelligent algorithm always has both merits in its specific formulation and deficiencies due to its inherent limitations. Therefore, we propose a mixture of these algorithms to create a new hybrid optimization algorithm known as the group search-artif...

In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima, Megiddo and Mizuno (A primal-dual infeasibleinterior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an a...

In this paper, an interior point approach is presented for linear programming problems by using the logarithmic barrier function method, which makes use of information on higher derivatives of the barrier function to explore search directions. The corresponding algorithm is derived, and can produce feasible successive iterations that have global convergence. The computational results indicate t...

In this paper we present a convergence analysis for some inexact (polynomial) variants of the infeasible-interior-point-algorithm of Kojima, Megiddo and Mizuno. For this analysis we assume that the iterates are bounded. The new variants allow the use of search directions that are calculated from the deening linear system with only moderate accuracy, e.g. via the use of Krylov subspace methods l...