Topology optimization problems often support multiple local minima due to a lack of
convexity. Typically, gradient-based techniques combined with continuation in model …

A class of risk-neutral generalized Nash equilibrium problems is introduced in which the
feasible strategy set of each player is subject to a common linear elliptic partial differential …

A novel generalization of Γ-convergence applicable to a class of equilibrium problems is
studied. After the introduction of the latter, a variety of its applications is discussed. The …

Variational inequalities can in general support distinct solutions. In this paper we study an
algorithm for computing distinct solutions of a variational inequality, without varying the initial …

The proximal Galerkin finite element method is a high-order, nonlinear numerical method
that preserves the geometric and algebraic structure of bound constraints in infinite …

We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype
for nonlocal partial differential equations, different from fractional powers of closed …

We develop a semismooth Newton framework for the numerical solution of fixed-point
equations that are posed in Banach spaces. The framework is motivated by applications in …

We consider the distributionally robust optimization and show that computing the
distributional worst-case is equivalent to computing the projection onto the canonical …

A multimaterial topology optimization framework using phase fields is suggested for the
simultaneous optimization of mechanical and optical properties to be used in the …

In the past decades, the optimal control of partial differential equations governed by partial
differential equations has made significant progress. This work concerns optimal control of …