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Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…

Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty.…

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…

In this paper, we explore how to leverage large language models (LLMs) to solve mathematical problems efficiently and accurately. Specifically, we demonstrate the effectiveness of classifying problems into distinct categories and employing…

In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the…

In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the…

We take a closer look at some theoretical challenges of Machine Learning as a function approximation, gradient descent as the default optimization algorithm, limitations of fixed length and width networks and a different approach to RNNs…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…

Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…

We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…

The problem of optimizing a linear objective function,given a number of linear constraints has been a long standing problem ever since the times of Kantorovich, Dantzig and von Neuman. These developments have been followed by a different…

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional…

Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…

Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…

Efficient and automated design of optimizers plays a crucial role in full-stack AutoML systems. However, prior methods in optimizer search are often limited by their scalability, generability, or sample efficiency. With the goal of…