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We consider the problem of recovering elements of a low-dimensional model from under-determined linear measurements. To perform recovery, we consider the minimization of a convex regularizer subject to a data fit constraint. Given a model,…
A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template…
We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism,…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
In this paper, the stability and stabilization problem of positive nonlinear systems, described by the Takagi-Sugeno discrete-time fuzzy model, is studied. The proposed approach is based on the linear co-positive Lyapunov function and…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the…
Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
This paper presents a convex approach to the optimization of a cooperative rendezvous, that is, the problem of two distant spacecraft that simultaneously operate to get closer. Convex programming guarantees convergence towards the optimal…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
The augmented Lagrangian method (ALM) is a benchmark for convex programming problems with linear constraints; ALM and its variants for linearly equality-constrained convex minimization models have been well studied in the literature.…
Control algorithms such as model predictive control (MPC) and state estimators rely on a number of different parameters. The performance of the closed loop usually depends on the correct setting of these parameters. Tuning is often done…