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In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…

Optimization and Control · Mathematics 2021-05-18 Gennaro Auricchio

We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…

Analysis of PDEs · Mathematics 2017-07-26 Gino Biondini , Thomas Trogdon

We proposed an algorithm for solving Hamilton-Jacobi equation associated to an optimal trajectory problem for a vehicle moving inside the pre-specified domain with the speed depending upon the direction of the motion and current position of…

Computer Vision and Pattern Recognition · Computer Science 2013-03-29 Myong-Song Ho , Gwang-Hui Ju , Yong-Bom O , Gwang-Ho Jong

In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…

Probability · Mathematics 2020-09-15 Qian Lin

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…

Analysis of PDEs · Mathematics 2009-04-08 Yousong Luo

We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of the…

Probability · Mathematics 2023-08-04 Andrea Cosso , Fausto Gozzi , Mauro Rosestolato , Francesco Russo

We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…

Optimization and Control · Mathematics 2021-10-08 Harbir Antil , Ciprian G. Gal , Mahamadi Warma

This paper deals with generalized differentiability and second-order necessary optimality conditions for a box-constrained optimal control problem governed by an exponential semilinear elliptic equation with discrete measures as sources,…

Optimization and Control · Mathematics 2026-05-20 Vu Huu Nhu , Nguyen Hai Son , Phan Quang Sang , Tran Duy

In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…

Optimization and Control · Mathematics 2025-10-14 Alessandro Calvia , Federico Cannerozzi , Giorgio Ferrari

Control barrier functions have shown great success in addressing control problems with safety guarantees. These methods usually find the next safe control input by solving an online quadratic programming problem. However, model uncertainty…

Systems and Control · Electrical Eng. & Systems 2020-11-24 Chuanzheng Wang , Yinan Li , Yiming Meng , Stephen L. Smith , Jun Liu

We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a…

Probability · Mathematics 2014-08-19 Robert C. Dalang , Laura Vinckenbosch

In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…

Optimization and Control · Mathematics 2017-11-27 Peyman Mohajerin Esfahani , Debasish Chatterjee , John Lygeros

We prove two duality descriptions of the value function for a generic stochastic optimal problem. These descriptions also hold when the diffusion is controlled, a case left open by the literature so far.

Optimization and Control · Mathematics 2026-02-23 Peter Bank , Filippo de Feo

The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of…

Optimization and Control · Mathematics 2024-11-07 Cyrille Kenne , Landry Djomegne , Pascal Zongo

The equivalence of time-optimal and distance-optimal control problems is shown for a class of parabolic control systems. Based on this equivalence, an approach for the efficient algorithmic solution of time-optimal control problems is…

Optimization and Control · Mathematics 2019-04-17 Lucas Bonifacius , Karl Kunisch

The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…

Optimization and Control · Mathematics 2022-07-22 Georgy Kostin , Alexander Gavrikov

Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…

Optimization and Control · Mathematics 2018-09-14 Lucas Bonifacius , Konstantin Pieper , Boris Vexler

In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…

Optimization and Control · Mathematics 2022-05-18 Eduardo Casas , Mariano Mateos

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…

Classical Analysis and ODEs · Mathematics 2015-12-22 Ricardo Almeida

We consider an optimal control problem governed by a semilinear PDE in cases where the optimal control is of bang-bang type. By utilizing the theory of Bessel potential space, we characterize quadratic growth of the objective via a…

Optimization and Control · Mathematics 2026-02-17 Gerd Wachsmuth