Related papers: Optimization methods for achieving high diffractio…

We present a design methodology for free-space beam-forming with general profiles from grating couplers which avoids the need for numerical optimization, motivated by applications in ion trap physics. We demonstrate its capabilities through…

In this paper, we study Newton-conjugate gradient (Newton-CG) methods for minimizing a nonconvex function $f$ whose Hessian is $(H_f,\nu)$-H\"older continuous with modulus $H_f>0$ and exponent $\nu\in(0,1]$. Recently proposed Newton-CG…

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed an optimized gradient method (OGM) for this problem and…

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

Dual descent methods are commonly used to solve network flow optimization problems, since their implementation can be distributed over the network. These algorithms, however, often exhibit slow convergence rates. Approximate Newton methods…

In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…

We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…

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 aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only…

In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…

This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…

We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…

The problem of optimizing the parameters of a laser pulse compressor consisting of four identical diffraction gratings is solved analytically. The goal of optimization is to obtain maximum pulse power, completely excluding both beam…

We present a theoretical framework and practical methodology for designing high-efficiency metagratings (MGs), sparse periodic arrangements of subwavelength polarizable particles (meta-atoms), on low-cost dielectric substrates with…

Electron backscatter diffraction (EBSD) is a well-established method of characterisation for crystalline materials. This technique can rapidly acquire and index diffraction patterns to provide phase and orientation information about the…

Dual descent methods are commonly used to solve network optimization problems because their implementation can be distributed through the network. However, their convergence rates are typically very slow. This paper introduces a family of…

We present a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective…

A thorough theoretical study of the optical properties of periodic Si nanosphere arrays is undertaken, placing particular emphasis on the synergy between electric and magnetic Mie resonances, which occur in high-refractive-index…

We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…

One-dimensional light harvesting structures with a realistic geometry nano-patterned on an opaque metallic film are optimized to render high transmission efficiencies at optical and infrared frequencies. Simple design rules are developed…