Tensor factorizations with nonnegative constraints have found application in analyzing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g., count data), which leads to sparse tensors that can be modeled by sparse factor matrices. In this paper we investigate efficient techniques for computing an app...

BACKGROUND Cardiac diseases represent the leading cause of sudden death worldwide. During the development of cardiac diseases, the left ventricle (LV) changes obviously in structure and function. LV motion estimation plays an important role for diagnosis and treatment of cardiac diseases. To estimate LV motion accurately for cine magnetic resonance (MR) cardiac images, we develop an algorithm b...

An efficient multi-block Newton–Krylov algorithm using the compressible Navier–Stokes equations is presented for the analysis and design of high-lift airfoil configurations. The preconditioned generalized minimum residual (GMRES) method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Furthermore, the GMRES method is used ...

In this paper, the performances of the quasi-Newton BFGS algorithm, the NEWUOA derivative free optimization algorithm, the CovarianceMatrix Adaptation Evolution Strategy (CMAES), the Differential Evolution (DE) algorithm and a Particle Swarm Optimization (PSO) algorithm are compared experimentally on benchmark functions reflecting important challenges encountered in real-world optimization prob...

One of the widely used methods for solving a nonlinear system of equations is the quasi-Newton method. The basic idea underlining this type of method is to approximate the solution of Newton's equation by means of approximating the Jacobian matrix via quasi-Newton update. Application of quasi-Newton methods for large scale problems requires, in principle, vast computational resource to form and...

The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss–Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this...

New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limitedmemory BFGS using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. T...

Aim at the class electromagnetic algorithm (EM) late for “mining” ability is insufficient, solution precision is not higher, and easy in premature problem, this paper proposes a combination of chaotic map and confined quasi-Newton (L-BFGS) local optimization operator of the chaotic class electromagnetism algorithm. Its main idea is in the late class electromagnetism algorithm using limit domain...

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

<span><span>Quasi-Newton methods are a class of numerical for </span>solving the problem unconstrained optimization. To improve overall efficiency resulting algorithms, we use quasi-Newton which is interesting equation. In this manuscript, present modified BFGS update formula based on new equation, give search direction solving optimizations proplems. We analyse convergence ra...