The semi-infinite programming problem(SIP) is an optimization problem having an infinite number of inequality constrains and a finite number of variables. Since many important problems in the real world can be formulated in a natural manner as SIPs, many researchers have developed theories and algorithms for solving SIPs. In recent years, special SIPs involving infinitely many conic constraints (SICP) have been studied extensively because of its interesting structure and wide applications. In this paper, we introduce two algorithms for solving SICPs and observe their specific properties concerning global and local convergences.

This paper presents a new methodology to compute the Greeks of barrier options. In particular, we develop chain rule(CR) for Wiener path integral between two curves that arise while computing the Greeks for barrier options. The boundary terms of CR, concentrated on the set of paths that touch one of the curves once, are specified. We also illustrate the effectiveness of our method through numerical examples.

Mammalian skin works as physical, chemical, and immunological defenses, keeping water inside and nuisances outside. Such barrier function is maintained in stratum corneum, the outermost layer composed of dead cells. We construct a mathematical model of the epidermal structure depending on dermal deformation in order to mathematically understand the mechanisms of homeostasis of the barrier function of the stratum corneum. Our mathematical model consists of Ca²⁺ dynamics, cells dynamics and basal membrane dynamics. Using these mathematical models, we aim at understanding of the homeostatic mechanism of the barrier function of the stratum corneum.