Related papers: Second-Order Newton-Based Extremum Seeking for Mul…
We propose novel policy search algorithms in the context of off-policy, batch mode reinforcement learning (RL) with continuous state and action spaces. Given a batch collection of trajectories, we perform off-line policy evaluation using an…
This paper studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints allowing to reformulate the original nonlinear system in the so-called…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
This paper deals with the gradient extremum seeking control for static scalar maps with actuators governed by distributed diffusion partial differential equations (PDEs). To achieve the real-time optimization objective, we design a…
In this paper, we investigate the problem of source seeking with a unicycle in the presence of local extrema. Our study is motivated by the fact that most of the existing source seeking methods follow the gradient direction of the signal…
This paper focuses on the further development of the Lie bracket approximation approach for extremum seeking systems. Classical results in this area provide extremum seeking algorithms with exponential convergence rates for quadratic-like…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix,…
In this paper we illuminate some algebraic-combinatorial structure underlying the second order networks (SONETS) random graph model of Nykamp, Zhao and collaborators. In particular we show that this algorithm is deeply connected with a…
Finding an approximate second-order stationary point (SOSP) is a well-studied and fundamental problem in stochastic nonconvex optimization with many applications in machine learning. However, this problem is poorly understood in the…
Stationary and instationary Stokes and Navier-Stokes flows are considered on two-dimensional manifolds, i.e., on curved surfaces in three dimensions. The higher-order surface FEM is used for the approximation of the geometry, velocities,…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
This paper considers decentralized dynamic optimization problems where nodes of a network try to minimize a sequence of time-varying objective functions in a real-time scheme. At each time slot, nodes have access to different summands of an…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
We consider the problem of finding an approximate second-order stationary point of a constrained non-convex optimization problem. We first show that, unlike the gradient descent method for unconstrained optimization, the vanilla projected…
This study introduces two second-order methods designed to provably avoid saddle points in composite nonconvex optimization problems: (i) a nonsmooth trust-region method and (ii) a curvilinear linesearch method. These developments are…
In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…
We present high-order, finite element-based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to…
We propose a new design strategy for extremum seeking control for a multi-dimensional single-integrator system in the presence of local extrema. The proposed method employs suitably designed sinusoidal dither signals, which force the…
We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i)…