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A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We propose a novel use of a broadcasting operation, which distributes univariate functions to all entries of the tensor covariate, to model the nonlinearity in tensor regression nonparametrically. A penalized estimation and the…
We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…
In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…
Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e. finding ground states). For both statistical mechanics and…
The emerging field of learning-augmented online algorithms uses ML techniques to predict future input parameters and thereby improve the performance of online algorithms. Since these parameters are, in general, real-valued functions, a…
Forecasting project expenses is a crucial step for businesses to avoid budget overruns and project failures. Traditionally, this has been done by financial analysts or data science techniques such as time-series analysis. However, these…
Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton…
This paper considers an online proximal-gradient method to track the minimizers of a composite convex function that may continuously evolve over time. The online proximal-gradient method is inexact, in the sense that: (i) it relies on an…
This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…
In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic…
Accurately selecting and estimating smooth functional effects in additive models with potentially many functions is a challenging task. We introduce a novel Demmler-Reinsch basis expansion to model the functional effects that allows us to…
This paper considers the distributed optimization of a sum of locally observable, non-convex functions. The optimization is performed over a multi-agent networked system, and each local function depends only on a subset of the variables. An…
This paper addresses a class of constrained optimization problems over networks in which local cost functions and constraints can be nonconvex. We propose an asynchronous distributed optimization algorithm, relying on the centralized Method…
In the recent years more and more high-dimensional data sets, where the number of parameters $p$ is high compared to the number of observations $n$ or even larger, are available for applied researchers. Boosting algorithms represent one of…
Boosting is a widely used machine learning approach based on the idea of aggregating weak learning rules. While in statistical learning numerous boosting methods exist both in the realizable and agnostic settings, in online learning they…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric…
This research focuses on the estimation of a non-parametric regression function designed for data with simultaneous time and space dependencies. In such a context, we study the Trend Filtering, a nonparametric estimator introduced by…
In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex)…