Related papers: Surface Growth Driven by an Optimality Criterion

We study discrete dynamics governed by a difference inclusion whose increment is the sum of a selection from a set-valued map and a noise term. For any bounded realization, convergence follows once the inter-iterate diameter is controlled…

We model the performance of an ideal closed chain of L processing elements that work in parallel in an asynchronous manner. Their state updates follow a generic conservative algorithm. The conservative update rule determines the growth of a…

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…

Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…

In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…

This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the…

This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…

A model for morphoelastic growth, that is, growth influenced by elastic stress, driven by the absorption of nutrients is considered. The model features a multiplicative decomposition of the deformation gradient into an elastic contribution…

We introduce a minimal model of solid-forming anisotropic molecules that displays, in thermal equilibrium, surface orientational order without bulk orientational order. The model reproduces the nonequilibrium behavior of recent experiments…

We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set…

We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…

Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…

In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…

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…

We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…

In this paper, we present a generic framework that allows accelerating almost arbitrary non-accelerated deterministic and randomized algorithms for smooth convex optimization problems. The main approach of our envelope is the same as in…

Geometrical cues are known to play a very important role in neuronal growth and the formation of neuronal networks. Here, we present a detailed analysis of axonal growth and dynamics for neuronal cells cultured on patterned…