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This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
We systematically develop a learning-based treatment of stochastic optimal control (SOC), relying on direct optimization of parametric control policies. We propose a derivation of adjoint sensitivity results for stochastic differential…
Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…
Differentially Private Stochastic Gradient Descent (DP-SGD) has been widely used for solving optimization problems with privacy guarantees in machine learning and statistics. Despite this, a systematic non-asymptotic convergence analysis…
This paper proposes a redundancy resolution algorithm for a redundant manipulator based on dynamic programming. This algorithm can compute the desired joint angles at each point on a pre-planned discrete path in Cartesian space, while…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
Decentralized optimization, particularly the class of decentralized composite convex optimization (DCCO) problems, has found many applications. Due to ubiquitous communication congestion and random dropouts in practice, it is highly…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
We study the unconstrained and the minimax saddle point variants of the convex multi-stage stochastic programming problem, where consecutive decisions are coupled through the objective functions, rather than through the constraints. We…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
Stochastic constraints, which incorporate both deterministic parameters and random variables, extend classical deterministic constraints by explicitly accounting for uncertainty. These constraints are increasingly prevalent in data science,…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…
As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
The type of decision dependent uncertainties (DDUs) imposes a great challenge in decision making, while existing methodologies are not sufficient to support many real practices. In this paper, we present a systematic study to handle this…
Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are…
In this paper, we propose a novel Dual Inexact Splitting Algorithm (DISA) for distributed convex composite optimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed with a linear…
Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform…