Related papers: Second-order Optimality Conditions for Time-Optima…
From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…
Along the optimal trajectory of an optimal control problem constrained by a semilinear parabolic partial differential equation, we prove the differentiability of the value function with respect to the initial condition and, under additional…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…
In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on the kind of problems arising for example when controlling the anisotropic Allen-Cahn equation as a model for crystal growth.…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…
In this paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive…
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,…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as generalized Black--Scholes models. We establish local null…
In this paper we consider the optimal control of semilinear fractional PDEs with both spectral and integral fractional diffusion operators of order $2s$ with $s \in (0,1)$. We first prove the boundedness of solutions to both semilinear…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…
In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization…