BACKGROUND Food product reformulation is seen as one among several tools to promote healthier eating. Reformulating the recipe for a processed food, e.g. reducing the fat, sugar or salt content of the foods, or increasing the content of whole-grains, can help the consumers to pursue a healthier life style. In this study, we evaluate the effects on calorie sales of a 'silent' reformulation strat...

In this paper, we examine a mixed integer linear programming (MILP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer variable with its binary expansion and then using McCormick envelopes to linearize the resul...

Globally, soda taxes are gaining momentum as powerful interventions to discourage sugar consumption and thereby reduce the growing burden of obesity and non-communicable diseases (NCDs). Evidence from early adopters including Mexico and Berkeley, California, confirms that soda taxes can disincentivize consumption through price increases and raise revenue to support government programs. The Unit...

Abstract In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on Hilbert into equivalent two-operator problems. Our approach relies Pierra’s classical with different decomposition, which results in reduction of the dimension outcoming space. We discuss case not necessarily convex feasibility and best approximation By applyi...

Variational inequalities over sets defined by systems of equalities and inequalities are considered. A new reformulation of the KKT-conditions of the variational inequality as a system of equations is proposed. A related unconstrained minimization reformulation is also investigated. As a by-product of the analysis, a new characterization of strong regularity of KKT-points is given.

This paper deals with the preliminary design problem when the product is modeled as an analytic model. The analytic models based method aims to use mathematical equations to address both multiphysic and economic characteristics of a product. The proposed approach is to convert the preliminary design problem into a global constrained optimization problem. The objective is to develop powerful opt...

In this work, we present a new Big-M reformulation for Generalized Disjunctive Programs. The proposed MINLP reformulation is stronger than the traditional Big-M, and it does not require additional variables or constraints. We present the new Big-M, and analyze the strength in its continuous relaxation compared to that of the traditional Big-M. The new formulation is tested by solving several in...