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The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…

Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

We empirically evaluate the finite-time performance of several simulation-optimization algorithms on a testbed of problems with the goal of motivating further development of algorithms with strong finite-time performance. We investigate if…

This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are…

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a…

We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…

The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing…

Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…

Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…

We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…

Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research…

This paper tackles the problem of discretizing accelerated optimization flows while retaining their convergence properties. Inspired by the success of resource-aware control in developing efficient closed-loop feedback implementations on…

Higher-order regularization problem formulations are popular frameworks used in machine learning, inverse problems and image/signal processing. In this paper, we consider the computational problem of finding the minimizer of the Sobolev…

Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…

Convex programming with linear constraints plays an important role in the operation of a number of everyday systems. However, absent any additional protections, revealing or acting on the solutions to such problems may reveal information…

When faced with a specific optimization problem, choosing which algorithm to use is always a tough task. Not only is there a vast variety of algorithms to select from, but these algorithms often are controlled by many hyperparameters, which…

Designing and analyzing optimization methods via continuous-time models expressed as ordinary differential equations (ODEs) is a promising approach for its intuitiveness and simplicity. A key concern, however, is that the convergence rates…

A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an…