Suchergebnisse

"Since quasiconvex functions have convex lower level sets it is possible to minimize them by means of separating hyperplanes. An example of such a procedure, well-known for convex functions, is the subgradient method. However, to nd the normal vector of a separating hyperplane is in general not easy for the quasiconvex case. This paper attempts to gain some insight into the computational aspects of determining such a normal vector and the geometry of lower level sets of quasiconvex functions. In order to do so, the directional di erentiability of quasiconvex functions is thoroughly studied. As a consequence of that study, it is shown that an important subset of quasiconvex functions belongs to the class of quasidifferentiable functions. The main emphasis is, however, on computing actual separators. Some important examples are worked out for illustration."

Whether your interests lie in scientific arenas, the corporate world, or in government, you have certainly heard the praises of big data: Big data will give you new insights, allow you to become more efficient, and/or will solve your problems. While big data has had some outstanding successes, many are now beginning to see that it is not the Silver Bullet that it has been touted to be. Here our main concern is the overall impact of big data; the current manifestation of big data is constructing a Maginot Line in science in the 21st century. Big data is not "lots of data" as a phenomena anymore; The big data paradigm is putting the spirit of the Maginot Line into lots of data. Big data overall is disconnecting researchers and science challenges. We propose No-Boundary Thinking (NBT), applying no-boundary thinking in problem defining to address science challenges.