Related papers: Contextual Strongly Convex Simulation Optimization…

Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…

This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative…

This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost…

We investigate the problem of online convex optimization with unknown delays, in which the feedback of a decision arrives with an arbitrary delay. Previous studies have presented a delayed variant of online gradient descent (OGD), and…

This paper proposes real-time sequential convex programming (RTSCP), a method for solving a sequence of nonlinear optimization problems depending on an online parameter. We provide a contraction estimate for the proposed method and, as a…

This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…

This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error…

We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…

This work concerns the zeroth-order global minimization of continuous nonconvex functions with a unique global minimizer and possibly multiple local minimizers. We formulate a theoretical framework for inexact proximal point (IPP) methods…

In this paper, we revisit the smooth and strongly-convex-strongly-concave minimax optimization problem. Zhang et al. (2021) and Ibrahim et al. (2020) established the lower bound $\Omega\left(\sqrt{\kappa_x\kappa_y} \log…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

We present a real-time-capable set-based framework for closed-loop predictive control of autonomous systems using tools from computational geometry, dynamic programming, and convex optimization. The control architecture relies on the…

We introduce \texttt{OPO-CMDP}, the first policy optimization algorithm for stochastic Contextual Markov Decision Process (CMDPs) under general offline function approximation. Our approach achieves a high probability regret bound of…

In the past few years, Online Convex Optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this paper, we propose new step-size rules and…

We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the positive quadrant of a…

We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…