A bstract This paper addresses itself to an algorithm for a convex minimization problem with an additional convex multiplicative constraint. A convex multiplicative constraint is such that a product of two convex functions is less than or equal to some constant. It is shown that this non convex problem can be solved by solving a sequence of convex programming problems. The basic idea of this al...

In this paper, we propose a new static analysis method which is applicable for a classical linear logic programming language. Andreoli et al. proposed a static analysis method for the classical linear logic programming language LO, but their method did not cover multiplicative connectives which are important for a resource-sensitive feature of linear logic. Our method, in contrast, covers multi...

We introduce the logic of bunched implications, BI, in which multiplicative (or linear) and additive (or intuitionistic) implications live side-by-side. We provide a truth conditional semantics, a proof theory and a categorical semantics of proofs. We explain how BI arises as a logic of resources and sketch a development of this computational interpretation, which is quite diierent from that of...

Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-aligned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and co...