Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization

Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations

A Newton's method for benchmarking time series

We present a Newton's method with Hessian modification for benchmarking a time series according to the Causey and Trager growth rates preservation principle. The proposed technique is easy to implement, computationally robust and efficient, all features which make it an effective statistical tool also in a data-production process involving a considerable amount of series

A multi-grid continuation strategy for parameter-dependent variational inequalities

AbstractFor parameter-dependent nonlinear elliptic obstacle problems a path-following multi-grid continuation strategy is developed combining a nested iteration type scheme as predictor with a subsequent multi-grid method as corrector. The performance of the algorithm is illustrated by some numerical results for the Bratu problem

Inner and outer loop optimization in semiconductor manufacturing supply chain management

Semiconductor manufacturing, Supply chain management, Model predictive control, Linear programming, Strategic planning, Tactical execution, Hierarchical decision-making,