Algorithmic Nonsmooth Optimization

Over the past thirty years there has been a growing need and interest for nonsmooth optimization methods. Nonsmoothness of objective or constraint functions may arise, for example, from heterogeneous material properties, from process controls and safety mechanisms that dynamically switch on and off; from variational inequality representations of free boundaries, phase transitions, contacts with friction; and from numerical schemes such as upwind finite differences and flux limiters. In multilevel optimization or very large scale applications nonsmoothness often arises by decomposition through the combinatorial nature of inequality constraints yielding piecewise smooth solution operators entering into the global objective. The participants of the school will be introduced to the relevant parts of nonsmooth analysis, the resulting optimality conditions in finite and infinite dimensions and the design of algorithms and software for their iterative solutions. Of particular concern are the numerical treatment of problems resulting from the discretization of differential equations.