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We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…
In this article, the minimum time control problem of an electric vehicle is modeled as a Mayer problem in optimal control, with affine dynamics with respect to the control and with state constraints. The candidates as minimizers are…
In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty re-formulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a non-zero…
We investigate the optimization of quantum control from a differential geometric perspective. In our approach, optimal control minimizes the cost associated with evolving a quantum state, with the cost quantified by the length of the…
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the…
As observed by Auderset et al. (2005) and Wiesel (2012), viewing covariance matrices as elements of a Riemannian manifold and using the concept of geodesic convexity provide useful tools for studying M-estimators of multivariate scatter. In…
We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
This paper presents a novel model predictive control strategy for controlling autonomous motion systems moving through an environment with obstacles of general shape. In order to solve such a generic non-convex optimization problem and find…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
In this paper we study optimal control problems in Wasserstein spaces, which are suitable to describe macroscopic dynamics of multi-particle systems. The dynamics is described by a parametrized continuity equation, in which the Eulerian…
In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…
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…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
We consider long term average or `ergodic' optimal control poblems with a special structure: Control is exerted in all directions and the control costs are proportional to the square of the norm of the control field with respect to the…
An optimal control problem subject to an elliptic obstacle problem is studied. We obtain a numerical approximation of this problem by discretising the PDE obtained via a Moreau--Yosida type penalisation. For the resulting discrete control…
We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…