Nonlinear Planning Model With a Gaussian Criterion of Optimization (Gaussian Programming Model)

TL;DR

This paper introduces a nonlinear planning model using a Gaussian optimality criterion, providing a more realistic representation of economic processes than traditional linear models, and offers approximation methods for practical implementation.

Contribution

It develops a novel nonlinear non-convex Gaussian programming model based on an economic-probabilistic analogy, expanding the modeling toolkit for complex economic systems.

Findings

Constructed a Gaussian utility and cost theory for economic modeling

Developed a nonlinear non-convex Gaussian programming model

Presented an approximation method using generalized piecewise-linear programming

Abstract

We propose an Economic - Probabilistic analogy: the category of cost is analogous to the category of Probability. The proposed analogy permits construction of an informal theory of nonlinear non-convex Gaussian Utility and Cost, which describes the real economic processes more adequately than a theory based on a linear and convex models. Based on the proposed analogy, we build a nonlinear non-convex planning model with a Gaussian optimality criterion - Gaussian Programming Model. We also describe a corresponding model of Generalized Piecewise-Linear Programming that can be used to approximate a Gaussian Programming model, and vice verse. Proposed constructions are illustrated on a numerical example.