A quasi-Newton algorithm for semi-infinite programming using an Leo exact penalty function is described, and numerical results are presented. Comparisons with three Newton algorithms and one other quasi-Newton algorithm show that the algorithm is very promising in practice. AMS classifications: 65K05,90C30.

In this paper, we investigate a formula to solve systems of the form (Bk + D)x = y, where Bk comes from a limited-memory BFGS quasi-Newton method and D is a diagonal matrix with diagonal entries di,i ≥ σ for some σ > 0. These types of systems arise naturally in large-scale optimization. We show that provided a simple condition holds on B0 and σ, the system (Bk + D)x = y can be solved via a recu...

We consider sequential quadratic programming (SQP) methods for solving constrained nonlinear programming problems. It is generally believed that SQP methods are sensitive to the accuracy by which partial derivatives are provided. One reason is that differences of gradients of the Lagrangian function are used for updating a quasi-Newton matrix, e.g., by the BFGS formula. The purpose of this pape...

We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer memory or data are collected in real-time). In our proposed framework, stochasticity is introduced in two different frameworks as a means to overcome these compu...

by considering the fact that the surface tension of a real fluid arises from a combination of both repulsive and attractive forces between molecules, a new expression for the interfacial tension has been derived from scaled particle theory (spt)  based on the work of cavity formation and the interaction energy between molecules. at the critical temperature, the interfacial tension between coexi...

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these disparate approaches by maintaining an independent Hessian approximation for each contributing function in the sum. We maintain computational tractability and limit ...

To diagnose the malignancy in thyroid tumor, neural network approach is applied and the performances of thirteen batch learning algorithms are investigated on accuracy of the prediction. Therefore, a back propagation feed forward neural networks (BP FNNs) is designed and three different numbers of neuron in hidden layer are compared (5, 10 and 20 neurons). The pathology result after the surgery...

We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthetic and real data experiments, that our approach offers advantages over the cl...

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Møller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter versio...