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Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…

In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…

Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…

In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…

The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how…

A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…

This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…

This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

We present a systematic derivation of the algorithms required for computing the gradient and the action of the Hessian of an arbitrary misfit function for large-scale parameter estimation problems involving linear time-dependent PDEs with…

The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…

The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the…

We present a novel approach for parameter calibration of the Heston model for pricing an Asian put option, namely space mapping. Since few parameters of the Heston model can be directly extracted from real market data, calibration to real…

This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…