Editorial: Vanishing methods

Guest Editorial: Formal Methods

We’d better start by defining terms, since the phrase Formal Methods (FM) can have a wide range of connotations in Computer Science. For the purpose of this Special Theme Issue, ‘Formal Methods’ means the use of mathematical techniques for the construction of computing systems, with a particular focus on the construction of industrial scale systems. The focus on large systems is significant. Th...

Formal Methods Guest Editorial

This introductory paper gives some historical background to the emergence of formal methods, overviews what subsequently happened, and surveys prospects for the future. Brief introductions to the remaining papers in the Special Issue are given.

Editorial: problem-solving methods

Vanishing Vanishing Cycles

If A• is a bounded, constructible complex of sheaves on a complex analytic space X, and f : X → C and g : X → C are complex analytic functions, then the iterated vanishing cycles φg[−1](φf [−1]A •) are important for a number of reasons. We give a formula for the stalk cohomology H∗(φg[−1]φf [−1]A •)x in terms of relative polar curves, algebra, and the normal Morse data and micro-support of A•.

Active-set Newton methods for mathematical programs with vanishing constraints

Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious difficulties in theoretical and numerical treatment of these problems. In this work, we suggest several glo...