Related papers: Surface Growth Driven by an Optimality Criterion
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The intentional growth of metastable surface structures of organic molecules adsorbed on inorganic substrates is a challenging task. It is usually unclear which kinetic mechanism leads to the metastable surface polymorph after a deposition…
For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…
The article presents a new method of linear programming, called the surface movement method. This method constructs an optimal objective path on the surface of the feasible polytope from the initial boundary point to the point at which the…
We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter…
In this paper, we study when we might expect the optimization curve induced by gradient descent to be \emph{convex} -- precluding, for example, an initial plateau followed by a sharp decrease, making it difficult to decide when optimization…
The paper concerns the necessary maximum principle for robust optimal control problems of quadratic BSDEs. The coefficient of the systems depends on the parameter $\theta$, and the generator of BSDEs is of quadratic growth in $z$. Since the…
This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
As a departure from existing continuum approaches for describing the stability and evolution of surfaces of crystalline materials, this article provides a description of surface evolution based on the physics of the main feature imposed by…
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
This paper studies the characteristics and applicability of the CutFEM approach as the core of a robust topology optimization framework for 3D laminar incompressible flow and species transport problems at low Reynolds number (Re < 200).…
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dimensional or structured problems, these global constants can…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…