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In this paper, we extend our previous results and formally propose the SCvx-fast algorithm, a new addition to the Successive Convexification algorithmic framework. The said algorithm solves non-convex optimal control problems with specific…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
In this paper we address the problem of decision making within a Markov decision process (MDP) framework where risk and modeling errors are taken into account. Our approach is to minimize a risk-sensitive conditional-value-at-risk (CVaR)…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte…
We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk…
This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
We consider the problem of learning control policies that optimize a reward function while satisfying constraints due to considerations of safety, fairness, or other costs. We propose a new algorithm, Projection-Based Constrained Policy…
We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functional. The first approach, proposed by Valmorbida et al. (IEEE…