Related papers: Optimal control problems with $L^0(\Omega)$ constr…
We study necessary optimality conditions for the deterministic mean field type free-endpoint optimal control problem. Our study relies on the Lagrangian approach that treats the mean field type control system as a crowd of infinitely many…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
Recently, there has been a surge of research on a class of methods called feedback optimization. These are methods to steer the state of a control system to an equilibrium that arises as the solution of an optimization problem. Despite the…
The modified Method of Successive Approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin Optimality Principle which, starting with an initial open loop…
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…
Time optimal control problems for some non-smooth systems in general form are considered. The non-smoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus,…
Given a sequential learning algorithm and a target model, sequential machine teaching aims to find the shortest training sequence to drive the learning algorithm to the target model. We present the first principled way to find such shortest…
In this paper, we study a stochastic optimal control problem under a type of consistent convex expectation dominated by G-expectation. By the separation theorem for convex sets, we get the representation theorems for this convex expectation…
We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…
In this paper we develop necessary conditions for optimality, in the form of the Pontryagin maximum principle, for the optimal control problem of a class of infinite dimensional evolution equations with delay in the state. In the cost…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…
The paper presents new sufficient conditions for the property of strong bi-metric regularity of the optimality map associated with an optimal control problem which is affine with respect to the control variable ({\em affine problem}). The…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…
We establish necessary conditions of optimality for discrete-time infinite-horizon optimal control in presence of constraints at infinity. These necessary conditions are in form of weak and strong Pontryagin principles. We use a functional…
We discuss contact geometry naturally related with optimal control problems (and Pontryagin Maximum Principle). We explore and expand the observations of [Ohsawa, 2015], providing simple and elegant characterizations of normal and abnormal…
An optimal guidance law for impact time control with field-of-view constraint is presented. The guidance law is derived by first converting the inequality-constrained nonlinear optimal control problem into an equality-constrained one…