We propose a bilevel optimization approach for the estimation of parameters in nonlocal
image denoising models. The parameters we consider are both the fidelity weight and …

Enhancers are short DNA regions bound with activators to increase gene transcription over
long distances. Hence, they play a crucial role in regulating eukaryotic gene expression …

Many inverse problems are phrased as optimization problems in which the objective
function is the sum of a data-fidelity term and a regularization. Often, the Hessian of the …

We present a new software system, PETSc TSAdjoint, for first-order and second-order
adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative …

We propose a bilevel optimization approach for the determination of parameters in nonlocal
image denoising. We consider both spatial weights in front of the fidelity term, as well as …

We present a modification of the limited memory BFGS (L-BFGS) method that ensures global
and linear convergence on nonconvex objective functions. Importantly, the modified method …

We present PNKH-B, a projected Newton--Krylov method for iteratively solving large-scale
optimization problems with bound constraints. PNKH-B is geared toward situations in which …

Abstract ℓ-BFGS is the state-of-the-art optimization method for many large scale inverse
problems. It has a small memory footprint and achieves superlinear convergence. The …

We devise an L-BFGS method for optimization problems in which the objective is the sum of
two functions, where the Hessian of the first function is computationally unavailable while the …

The Portable Extensible Toolkit for Scientific Computation (PETSc) library provides scalable
solvers for nonlinear time-dependent differential and algebraic equations and for numerical …