Related papers: A Class of Convex Optimization-Based Recursive Alg…
Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak 2006]. The proposed algorithm efficiently escapes saddle points and finds approximate local minima for general…
Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…
The geometric problem of estimating an unknown compact convex set from evaluations of its support function arises in a range of scientific and engineering applications. Traditional approaches typically rely on estimators that minimize the…
This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…
This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…
This paper considers time-average stochastic optimization, where a time average decision vector, an average of decision vectors chosen in every time step from a time-varying (possibly non-convex) set, minimizes a convex objective function…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…
This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…
In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an…