Related papers: A robust, discrete-gradient descent procedure for …
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
The present paper aims at providing a numerical strategy to deal with PDE-constrained optimization problems solved with the adjoint method. It is done through out a unified formulation of the constraint PDE and the adjoint model. The…
In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
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 is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by the discontinuous Galerkin (dG) method. An efficient and…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
In this paper, we study ordinary differential equations (ODE) coupled with solutions of a stochastic nonsmooth convex optimization problem (SNCOP). We use the regularization approach, the sample average approximation and the time-stepping…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
We present and mathematically analyze an online adjoint algorithm for the optimization of partial differential equations (PDEs). Traditional adjoint algorithms would typically solve a new adjoint PDE at each optimization iteration, which…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. A sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…