Research on multigrid methods for optimization problems is reviewed. Optimization problems include shape design, parameter optimization, and optimal control problems governed by partial differential equations of elliptic, parabolic, and hyperbolic type.

This paper compares three different global indirect approaches for solving the problem of finding optimal trajectories for low thrust spacecraft. The three methods tested were downhill simplex, genetic algorithms and simulated annealing. Two problems are analyzed. The first is a planar low thrust problem. This is the problem of finding a minimum time trajectory from Earth to Mars orbit using a ...

The paper is an introduction to the optimization methods of the linear accelerator cavity control system. Three distinct time periods of cavity operation are considered; filling with the EM field energy, field stabilization for the accelerated beam, and field decay. These periods are considered as different states of the cavity corresponding to adequate solutions of differential equation modeli...

Many intrusions which attempt to compromise the security of computer and network systems manifest themselves in changes in the intensity of events. Because of the ability of exponentially weighted moving average (EWMA) statistics to monitor the rate of occurrences of events based on their intensity, this technique is appropriate for implementation in control limits based algorithms. The researc...

In this paper, we propose to enhance particle-based stochastic optimization methods (SO) by using Principal Component Analysis (PCA) to build an approximation of the cost function in a neighborhood of particles during optimization. Then we use it to shift the samples in the direction of maximum cost change. We provide theoretical basis and experimental results showing that such enhancement impr...

Thesis: when a specific problem of optimization is " canonical " , i.e. works with " just the right concepts " and reflects " just the right questions " , then intrinsic tools are the way forward to insight.

This article describes the current state of the art of interior-point methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twenty years.

Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the optimization problem into the preparation of a low-temperature thermal state of the system. Motivated by the quantum annealing method, we present three strategies to ...

This tutorial describes a logic based approach to formulating and solving pure and mixed integer programming problems It develops logical counterparts for ideas associated with traditional branch and cut methods such as cutting planes facet de ning cuts re laxations etc The motivations for doing this are a to exploit the structure of a wide range of problems that are too complex for polyhedral ...

The paper deals with a problem encountered in the physical implementation of circuits on the PCB and VLSI chip level as well. Due to its complexity a decomposition methods are used to decrease the complexity of the problem. We present min-cut algorithms that are based upon the principle of partitioning. The circuit is repeatedly divided into densely connected subcircuits such that the number of...