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In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the…

This work quantifies the safety of trajectories of a dynamical system by the perturbation intensity required to render a system unsafe (crash into the unsafe set). Computation of this measure of safety is posed as a peak-minimizing optimal…

This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form $f+h$ where $h$ is a proper closed convex function,…

Reinforcement learning algorithms commonly seek to optimize policies for solving one particular task. How should we explore an unknown dynamical system such that the estimated model globally approximates the dynamics and allows us to solve…

Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy exploration is relatively well understood,…

Directional motion towards a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the control and predictive performance of system…

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…

Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…

Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…

We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…

The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss…

We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…

Accurate power system state estimation (PSSE) is an essential prerequisite for reliable operation of power systems. Different from static PSSE, dynamic PSSE can exploit past measurements based on a dynamical state evolution model, offering…

We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA.…

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…

During the past sixty years, a lot of effort has been made regarding the productive efficiency. Such endeavours provided an extensive bibliography on this subject, culminating in two main methods, named the Stochastic Frontier Analysis…

In this paper, we address tracking of a time-varying parameter with unknown dynamics. We formalize the problem as an instance of online optimization in a dynamic setting. Using online gradient descent, we propose a method that sequentially…

We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…