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This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…
We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…
We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of…
In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. Two discontinuous…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…
This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…
We propose a two-scale neural network method for optimal control problems governed by convection-dominated convection-diffusion-reaction equations. Building on two-scale architectures developed for singularly perturbed forward problems, we…
We consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set a strictly convex quadratic function, whose Hessian depends on the leader's decision. The resulting random variable is…
Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional…
This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using multi-agents with Markov switched network dynamics and noisy inter-agent communications. Unlike…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
Distributed optimization advances centralized machine learning methods by enabling parallel and decentralized learning processes over a network of computing nodes. This work provides an accelerated consensus-based distributed algorithm for…