Various problems in nonnegative quadratic programming arise in the training of large margin classifiers. We derive multiplicative updates for these problems that converge monotonically to the desired solutions for hard and soft margin classifiers. The updates differ strikingly in form from other multiplicative updates used in machine learning. In this paper, we provide complete proofs of conver...

In this paper we propose a Fully Polynomial Time Approximation Scheme (FPTAS) for a class of optimization problems where the feasible region is a polyhedral one and the objective function is the sum or product of linear ratio functions. The class includes the well known ones of Linear (Sum-of-Ratios) Fractional Programming and Multiplicative Programming.

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...

This paper interprets an image space accelerating branch and bound algorithm for globally solving a class of multiplicative programming problems (MP). In this algorithm, in order to obtain the global optimal solution, problem (MP) is transformed into equivalent (P2) by introducing new variables. By utilizing linearizing relaxation technique, can be converted series linear problems, which provid...

In [14] nonstandard analysis was used to construct a (standard) global attractor for the 3D stochastic Navier–Stokes equations with general multiplicative noise, living on a Loeb space, using Sell’s approach [26]. The attractor had somewhat ad hoc attracting and compactness properties. We strengthen this result by showing that the attractor has stronger properties making it a neo-attractor – a ...

A simplicial branch and bound duality-bounds algorithm is presented to globally solving the linear multiplicative programming (LMP).We firstly convert the problem (LMP) into an equivalent programming one by introducing p auxiliary variables. During the branch and bound search, the required lower bounds are computed by solving ordinary linear programming problems derived by using a Lagrangian du...