Related papers: A Lagrange Multiplier Method for Semilinear Ellipt…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
This paper proposes a multiblock alternating direction method of multipliers for solving a class of multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. We employ a majorization minimization procedure in…
This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of…
A distributed optimal control problem with final observation for a three- dimensional Lagrange averaged Navier-Stokes-? model is studied. The solvability of the optimal control problem is proved and the first-order optimality conditions are…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal…
High-amplitude free stream turbulence and surface roughness elements can excite a laminar boundary layer flow sufficiently to cause streamwise oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise…
We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a…
A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
In this paper we study an optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. The equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions. We…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie…
We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…
In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which proves that under rather mild assumptions, $x$ is a weak…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…