This paper describes a reduced quasi-Newton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced Hessian of the Lagrangian. A new approach is proposed in this paper. The idea is to search for the next itera...

This article investigates the stability analysis of discrete-time neural networks with time-varying delays by utilization quadratic delay information. First, three extended negative-definiteness lemmas for matrix-valued function different matrices injection are established. Second, a novel delay-product-type Lyapunov functional asymmetric summation is developed to relax positive-definiteness fu...

Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qual­ itative property called product synergy. The current definition of product synergy is insuf­ ficient for intercausal reasoning where there are additional uninstantiated causes of the common effect. We propose a new defi...