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In this paper, we prove the output feedback stabilization for the linearized Korteweg-de Vries (KdV) equation posed on a finite domain in the case the full state of the system cannot be measured. We assume that there is a sensor at the left…
A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…
Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
This paper analyses discontinuous Galerkin finite element methods (DGFEM) to approximate a regular solution to the von K\'arm\'an equations defined on a polygonal domain. A discrete inf-sup condition sufficient for the stability of the…
We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the…
This study introduces two second-order methods designed to provably avoid saddle points in composite nonconvex optimization problems: (i) a nonsmooth trust-region method and (ii) a curvilinear linesearch method. These developments are…
When the objective function is not locally Lipschitz, constraint qualifications are no longer sufficient for Karush-Kuhn-Tucker (KKT) conditions to hold at a local minimizer, let alone ensuring an exact penalization. In this paper, we…
We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to…
In this paper, we develop a regularized higher-order Taylor based method for solving composite (e.g., nonlinear least-squares) problems. At each iteration, we replace each smooth component of the objective function by a higher-order Taylor…
We establish a geometric condition guaranteeing exact copositive relaxation for the nonconvex quadratic optimization problem under two quadratic and several linear constraints, and present sufficient conditions for global optimality in…
We generalize the successive continuation paradigm introduced by Kern\'evez and Doedel [16] for locating locally optimal solutions of constrained optimization problems to the case of simultaneous equality and inequality constraints. The…
We present a computer assisted method for generating existence proofs and a posteriori error bounds for solutions to two point boundary value problems (BVPs). All truncation errors are accounted for and, if combined with interval arithmetic…
We analyze backward step control globalization for finding zeros of G\^ateaux-differentiable functions that map from a Banach space to a Hilbert space. The results include global convergence to a distinctive solution characterized by…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…
We prove that the full spectral picture of a transfer operator (every isolated eigenvalue, eigenvector, and Riesz projector outside the essential spectral radius) can be approximated to arbitrary precision by finite-rank discretizations,…
In this paper we introduce the notions of critical and noncritical multipliers for subdifferential variational systems extending to a general framework the corresponding notions by Izmailov and Solodov developed for classical…
In this paper, we design Dirichlet-Neumann boundary feedback controllers for the Korteweg-de Vries (KdV) equation that act at the right endpoint of the domain. The length of the domain is allowed to be critical. Constructing backstepping…
Derivative based optimization methods are efficient at solving optimal control problems near local optima. However, their ability to converge halts when derivative information vanishes. The inference approach to optimal control does not…