Related papers: Second-order sensitivity relations and regularity …
We investigate differentiability and subdifferentiability properties of the solution mapping associated with variational inequalities (VI) of the second kind involving the discrete total-variation. Bouligand differentiability of the…
Using min-max inequality we investigate the existence of solutions and thier dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle…
Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…
Adaptive optimal control using value iteration (VI) initiated from a stabilizing policy is theoretically analyzed in various aspects including the continuity of the result, the stability of the system operated using any single/constant…
We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the…
We consider a second order, two-point, singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and we obtain regularity results for its solution. First we establish classical…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Adaptive optimal control using value iteration initiated from a stabilizing control policy is theoretically analyzed in terms of stability of the system during the learning stage without ignoring the effects of approximation errors. This…
We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a…
This work establishes sensitivities of the solution of an optimal control problem (OCP) and a corresponding quantity of interest (QoI) to perturbations in a state/control-dependent component function that appears in the governing ODEs and…
A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular…
We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…
The unconstrained minimization of a sufficiently smooth objective function $f(x)$ is considered, for which derivatives up to order $p$, $p\geq 2$, are assumed to be available. An adaptive regularization algorithm is proposed that uses…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the…
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual…
This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…