Control Applications – Page 15 – Optimization Online

Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

Published: 2003/03/31

Control Applications, Linear, Cone and Semidefinite Programming control theory, infinite-dimensional problems, interior point methods, primal-dual algorithms, second-order cone programming

We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for “infinite-dimensional second-order cone programs.” We consider as an example a … Read more

Robust regularization

Published: 2002/09/19, Updated: 2002/09/23

Adrian Lewis

Control Applications, Nonsmooth Optimization, Robust Optimization locally lipschitz, nonsmooth analysis, prox-regularity, pseudospectrum, regularization, robust control, robust optimization, semi-algebraic, semidefinite representable

Given a real function on a Euclidean space, we consider its “robust regularization”: the value of this new function at any given point is the maximum value of the original function in a fixed neighbourhood of the point in question. This construction allows us to impose constraints in an optimization problem *robustly*, safeguarding a constraint … Read more

Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming

Published: 2002/08/15, Updated: 2003/05/29

J B Rawlings

M. J. Tenny

Stephen Wright

Chemical Engineering, Constrained Nonlinear Optimization, Control Applications model predictive control, nonlinear programming, sequential quadratic programming

Model predictive control requires the solution of a sequence of continuous optimization problems that are nonlinear if a nonlinear model is used for the plant. We describe briefly a trust-region feasibility-perturbed sequential quadratic programming algorithm (developed in a companion report), then discuss its adaptation to the problems arising in nonlinear model predictive control. Computational experience … Read more

TfMin: Short Reference Manual

Published: 2002/07/23

Jean-Baptiste Caillau

Joseph Noailles

Joseph Gergaud

Control Applications continuation, continuous minimum-time orbit transfer, low-thrust transfer, single shooting

This is a short guide to use the Fortran and Matlab package TfMin designed for the numerical solution of continuous 3D minimum-time orbit transfer around the Earth (with free final longitude), especially for low thrust engines. The underlying method is single shooting. The Matlab interface with the solver allows the user to define the problem … Read more

User’s Guide for SeDuMi Interface 1.01

Published: 2001/11/06

Didier Henrion

Yann Labit

Dimitri Peaucelle

Control Applications, Semi-definite Programming builder, lmi, parser, sedumi

A user-friendly free Matlab package for defining Linear Matrix Inequality (LMI) problems. It acts as an interface for the Self-Dual-Minimisation package SeDuMi developed by Jos F. Sturm. The functionalities of SeDuMi Interface are the following: (1) Declare an LMI problem. Five Matlab functions allow to define completely an LMI problem which can be characterised by … Read more

Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems

Published: 2001/09/27

Jie Sun

Defeng Sun

Control Applications, Nonsmooth Optimization eigenvalues, inverse eigenvalue problems, newton's methods, quadratic convergence, strong semismoothness, symmetric matrices

It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions. This directly implies that the eigenvalues of a symmetric matrix are semismooth everywhere. Based on a very recent … Read more

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

Published: 2001/02/01, Updated: 2021/11/02

Jean-Baptiste Caillau

Joseph Noailles

Control Applications adaptive discretization, finite differences, grid refinement, two-point linear boundary value problems, wavelet analysis

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