We study and compare preconditioners available for network interior point methods. We derive upper bounds for the condition number of the preconditioned matrices used in the solution of systems of linear equations defining the algorithm search directions. The preconditioners are tested using PDNET, a state-of-the-art interior point code for the minimum cost network flow problem. … Read more
We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunistic platform provided by the Condor system. The algorithms are of master-worker … Read more
The floorplanning (or facility layout) problem consists in finding the optimal positions for a given set of modules of fixed area (but perhaps varying dimensions) within a facility such that the distances between pairs of modules that have a positive connection cost are minimized. This is a hard discrete optimization problem; even the restricted version … Read more
This paper studies recent modifications of the limited memory BFGS (L-BFGS) method for solving large scale unconstrained optimization problems. Each modification technique attempts to improve the quality of the L-BFGS Hessian by employing (extra) updates in certain sense. Because at some iterations these updates might be redundant or worsen the quality of this Hessian, this … Read more
Self-scaled barrier functions are fundamental objects in the theory of interior-point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self-scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with a decomposition … Read more
In this paper, wavelet techniques are employed for the fast numerical solution of a control problem governed by an elliptic boundary value problem with boundary control. A quadratic cost functional involving natural norms of the state and the control is to be minimized. Firstly the constraint, the elliptic boundary value problem, is formulated in an … Read more
This paper proposes a new predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished features of the method are full use of the BFGS quasi-Newton method in the corrector procedure and an application of the conjugate gradient method with an effective … Read more
Long-term hydrothermal coordination is one of the main problems to be solved by an electric utility. Its solution provides the optimal allocation of hydraulic, thermal and nuclear resources at the different intervals of the planning horizon. The purpose of the paper is twofold. Firstly, it presents a new package for solving the hydrothermal coordination problem. … Read more
CSDP is a software package that implements the XZ primal–dual interior point method for semidefinite programming. In this method there are a number of computationally intensive steps including the construction of the Schur complement matrix $O$, the factorization of $O$, multiplications of matrices of size $n$ and Cholesky factorizations of matrices of size $n$. Profiling … Read more
Self-scaled barrier functions on self-scaled cones were introduced through a set of axioms in 1994 by Y.E. Nesterov and M.J. Todd as a tool for the construction of long-step interior point algorithms. This paper provides firm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains … Read more