In this paper, we consider multiplicative linear logic (MLL) from an automated deduction point of view. Linear logic is more expressive than classical and intuitionistic logic and has an undirectional character due to the particular treatment of negation and the absence of structural rules. Considering this new logical framework to make logic programming or programming with proofs (extracting p...

We shall extend Iri's multiplicative penalty function method for linear programming [41 so that it can handle the problem of unknown optimum value of the objective function, without solving both primal and dual problems simultaneously, and generate convergent dual solutions. By making use of these dual variables, lower bounds of the optimum objective function value are updated efficiently, whic...

We consider a branch-and-reduce approach for solving generalized linear multiplicative programming. First, a new lower approximate linearization method is proposed; then, by using this linearization method, the initial nonconvex problem is reduced to a sequence of linear programming problems. Some techniques at improving the overall performance of this algorithm are presented. The proposed algo...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

This paper proposes a multiplicative approach to solve defective issues in lexicographic goal programming of the analytic hierarchy process (LGPAHP). Although the LGPAHP can handle inconsistent interval comparison matrices, it generates different weights in the upper and lower triangular interval judgments. Instead of adopting additive constraints, the proposed method uses multiplicative constr...

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Nonnegativity constraints arise frequently in statistical learning and pattern recognition. Multiplicative updates provide natural solutions to optimizations involving these constraints. One well known set of multiplicative updates is given by the ExpectationMaximization algorithm for hidden Markov models, as used in automatic speech recognition. Recently, we have derived similar algorithms for...

Multiplicative update rules have proven useful in many areas of machine learning. Simple to implement, guaranteed to converge, they account in part for the widespread popularity of algorithms such as nonnegative matrix factorization and Expectation-Maximization. In this paper, we show how to derive multiplicative updates for problems in L1-regularized linear and logistic regression. For L1–regu...