Minh N. Dao

Parametric Robust Structured Control Design

We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case H∞ norm over a pre-specified set of uncertain parameters. At the core of our method is a nonsmooth minimization method tailored to functions which are semi-infinite minima of smooth functions. A rich test bench and a more detailed example illustrate the potential of the technique, which can deal with complex problems involving multiple possibly repeated uncertain parameters.

On Slater's condition and finite convergence of the Douglas---Rachford algorithm for solving convex feasibility problems in Euclidean spaces

The Douglas–Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility problems. Our analysis builds upon, and considerably extends, pioneering work by Spingarn. Specifically, we obtain finite convergence in the presence of Slater’s condition in the affine-polyhedral and in a hyperplanar-epigraphical case. Various examples illustrate our results. Numerical experiments demonstrate the competitiveness of the Douglas–Rachford algorithm for solving linear equations with a positivity constraint when compared to the method of alternating projections and the method of reflection–projection.

On the Finite Convergence of the Douglas--Rachford Algorithm for Solving (Not Necessarily Convex) Feasibility Problems in Euclidean Spaces

Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence. Numerous examples illustrate our results.

Nonconvex bundle method with application to a delamination problem

Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the stress field along the contact boundary. This leads to a hemivariational inequality, which after discretization by finite elements we solve by a nonconvex bundle method, where upper-

The Douglas-Rachford algorithm in the affine-convex case

C^1

Minimizing memory effects of a system

C1 criteria have to be minimized. As this is in contrast with other classes of mechanical problems with non-monotone friction laws and in other applied fields, where criteria are typically lower-

Proximal point algorithm, Douglas-Rachford algorithm and alternating projections: a case study

C^1