Related papers: A nonsmooth optimization approach for hemivariatio…
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…
This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformulating the contact problem as a nonlinear variational…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
We study the adhesive contact between elastic solids with randomly rough, self affine fractal surfaces. We present molecular dynamics (MD) simulation results for the interfacial stress distribution and the wall-wall separation. We compare…
Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
In this paper, we study a new variant of Moreau's sweeping process with velocity constraint. Based on an adapted version of Moreau's catching-up algorithm, we show the well-posedness (in the sense existence and uniqueness) of this problem…
We consider the problem of optimizing the sum of a smooth, nonconvex function for which derivatives are unavailable, and a convex, nonsmooth function with easy-to-evaluate proximal operator. Of particular focus is the case where the smooth…
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…
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…
We formulate and study two mathematical models of a thermoforming process involving a membrane and a mould as implicit obstacle problems. In particular, the membrane-mould coupling is determined by the thermal displacement of the mould that…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
It is well-known by now that the BFGS method is an effective method for minimizing nonsmooth functions. However, despite its popularity, theoretical convergence results are almost non-existent. One of the difficulties when analyzing the…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…
This paper presents an application of Canonical duality theory to the solution of contact problems with Coulomb friction. The contact problem is formulated as a quasi-variational inequality which solution is found by solving its…
The error incurred in the representation of the contact pressure at the edges of incomplete contacts by first order asymptotes is treated, and the maximum value of the relative error found for a range of geometries, both symmetric and…
A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedgeshaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. By using methods of the theory…
Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A…