Related papers: Second Order Necessary Conditions for Optimal Cont…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
In this paper, we are concerned with optimal control problems evolved on Riemannian manifolds, where the initial and final states satisfy some inequality and equality type constraints, and the control set is a separable metric space. We…
In this paper, we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds. We first obtain the second-order necessary conditions for weak Pareto optimal solutions for…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
In this paper, we establish some second order necessary/sufficient optimality conditions for optimal control problems of stochastic evolution equations in infinite dimensions. The control acts on both the drift and diffusion terms and the…
The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…
We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
Second-order necessary conditions for optimal control problems are considered, where the ``second-order" is in the sense of that Pontryagin's maximum principle is viewed as a first-order necessary optimality condition. A sufficient…
In this paper, we study a natural optimal control problem associated to the Paneitz obstacle problem on closed 4-dimensional Riemannian manifolds. We show the existence of an optimal control which is an optimal state and induces also a…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
The first part of the paper studies a class of optimal control problems in Bolza form, where the dynamics is linear w.r.t.~the control function. A necessary condition is derived, for the optimality of a trajectory which starts at a…
This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region…
An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control. The well-known Pontryagin type maximum principle for…
This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex,…
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…