We propose an approach to two-stage linear optimization with recourse that does not in-volve a probabilistic description of the uncertainty and allows the decision-maker to adjust the degree of conservativeness of the model, while preserving its linear properties.

We describe an efficient method for solving an optimal control problem that arises in robust model-predictive control. The problem is to design the input sequence that minimizes the peak tracking error between the ouput of a linear dynamical system and a desired target output, subject to inequality constraints on the inputs.

1.1 Robust linear programming In this section, we will be looking at the basic case of robust linear programming. We will consider two types of uncertainty sets: polytopic and ellipsoidal. A robust LP is a problem of the form: min. x cTx (1) s.t. aT i x b i; 8a i2U a i; 8b i2U b i;i= 1;:::;m; where U a i Rn and U b i R are given uncertainty ...

Robust Optimization • definitions of robust optimization • robust linear programs • robust cone programs • chance constraints EE364b, Stanford University

Mar 24, 2009 · We propose an approach to linear optimization with recourse that does not involve a probabilistic description of the uncertainty, and allows the decision-maker to adjust the degree of robustness of the model while preserving its linear properties.

We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs. Index Terms—Robust optimization, linear programming, semidefinite programming, dynamical systems.

Sep 25, 2014 · This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of...

Conic linear programming (CLP), and in particular, semidefinite programming (SDP), has received a lot of attention in recent years. Such a popularity can partly be attributed to the wide applicability of CLP, as well as recent advances in the design of provably efficient interior–point algorithms.

Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the …

Jan 1, 2002 · Numerical algorithms for linear and quadratic programming have been applied to optimal control since the 60s, and are widely used in model-predictive control, see (Morari and Lee 1999, Rawlings 2000).