WASP: a Wavelet Adaptive Solver for boundary value Problems – Short Reference Manual

This is a short guide to use the Matlab package WASP designed for the numerical solution of two-point linear boundary value problems that arise typically in linear quadratic optimal control. The method relies upon an adaptive computation of discretization based on a wavelet analysis. On a given refined grid, finite differences of various order are … Read more

Convex optimization problems involving finite autocorrelation sequences

We discuss convex optimization problems where some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density, which results in … Read more

Handling Nonnegative Constraints in Spectral Estimation

We consider convex optimization problems with the constraint that the variables form a finite autocorrelation sequence, or equivalently, that the corresponding power spectral density is nonnegative. This constraint is often approximated by sampling the power spectral density, which results in a set of linear inequalities. It can also be cast as a linear matrix inequality … Read more

Optimal Control of Distributed Proceses using Reduced Order Models

The open loop optimal control (dynamic optimization) of distributed parameter systems is considered here. These problems are usually solved by the Control Vector Parameterization (CVP) approach, which transforms the original dynamic optimization method into an outer nonlinear programming problem, which requires the solution of an inner initial value problem (IVP). The solution of this IVP … Read more

Improved linear programming bounds for antipodal spherical codes

Let $S\subset[-1,1)$. A finite set $C=\{x_i\}_{i=1}^M\subset\Re^n$ is called a {\em spherical S-code} if $||x_i||=1$ for each $i$, and $x_i^T x_j\in S$, $i\ne j$. For $S=[-1,.5]$ maximizing $M=|C|$ is commonly referred to as the {\em kissing number} problem. A well-known technique based on harmonic analysis and linear programming can be used to bound $M$. We consider … Read more

Semismooth Support Vector Machines

The linear support vector machine can be posed as a quadratic program in a variety of ways. In this paper, we look at a formulation using the two-norm for the misclassification error that leads to a positive definite quadratic program with a single equality constraint when the Wolfe dual is taken. The quadratic term is … Read more

iNEOS : An Interactive Environment for Nonlinear Optimization

In this paper we describe iNEOS, an Internet-based environment which facilitates the solution of complex nonlinear optimization problems. It enables a user to easily invoke a remote optimization code without having to supply the model to be optimized. An interactive communication between client and server is established and maintainted using CORBA. We test the system … Read more

Interior point methods for massive support vector machines

We investigate the use of interior point methods for solving quadratic programming problems with a small number of linear constraints where the quadratic term consists of a low-rank update to a positive semi-definite matrix. Several formulations of the support vector machine fit into this category. An interesting feature of these particular problems is the volume … Read more