Toru Higuchi

Life Cycle Management in Supply Chains: Identifying Innovations Through the Case of the VCR

As the supply chain is the major arena for competition in modern business, and at each stage in the industrial life cycle it is necessary to adjust the management of the supply chain to remain competitive, there is a growing demand for authoritative research to clarify the supply chain structure and evolution through the industrial life cycle. Life Cycle Management in Supply Chains: Identifying Innovations Through the Case of the VCR presents comprehensive, in-depth coverage of the intimate connection between the industry life cycle and supply chain management, utilizing the case of the industrial life cycle of the VCR to provide practitioners and researchers with key insight into the supply chain as the basic business unit for competition, and the requisite alteration of the management of the supply chain at each stage of the life cycle.

Function optimisation and Brouwer Fixed-Points on acute convex sets

The Brouwer Fixed-Point (FP) theorem is as follows. Given a continuous function φ(x) defined on a convex compact set S such that φ(x) lies in S then, there exists a point x* in S such that φ(x*) = x*. It is well-known that many optimisation problems can be cast as problems of finding a Brouwer FP. Instead, we propose an approach to the reverse problem of finding an FP by optimisation. First, we define acuteness for convex sets and propose an algorithm for computing a Brouwer FP based on a direction of ascent of what we call a hypothetical function. The algorithm uses 1D search as in the Frank–Wolfe algorithm. We report on numerical experiments comparing results with the Banach-iteration or successive-substitution method. The proposed algorithm is convergent for some challenging chaos-based examples for which the Banach-iteration approach fails.