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We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex…
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…
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 investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…
The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
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…
In this work, we study an optimal boundary control for the stochastic Allen Cahn Navier Stokes system. The governing system of nonlinear partial differential equations consists of the stochastic Navier Stokes equations with non homogeneous…
The Alternating Current Optimal Transmission Switching (ACOTS) problem incorporates line switching decisions into the AC Optimal Power Flow (ACOPF) framework, offering well-known benefits in reducing operational costs and enhancing system…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
This paper aims at solving an optimal control problem governed by an anisotropic Allen-Cahn equation numerically. Therefore we first prove the Fr\'echet differentiability of an in time discretized parabolic control problem under certain…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value…
A $\mathcal{H}_2$-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where $\ell_0$-penalty is added into the $\mathcal{H}_2$ cost to…
We consider a class of monotone systems in which the control signal multiplies the state. Among other applications, such bilinear systems can be used to model the evolutionary dynamics of HIV in the presence of combination drug therapy. For…