scholarly journals A Foundation for Logarithmic Utility Function of Money

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 665
Author(s):  
Francisco J. Navarro-González ◽  
Yolanda Villacampa
Keyword(s):  
Utility Function ◽  
Optimization Problem ◽  
Utility Functions ◽  
Time Interval ◽  
System Of Equations ◽  
Logarithmic Function ◽  
Total Utility ◽  
Perishable Goods ◽  
The Matrix ◽  
Derivatives Of

This paper presents a study on the optimization problem of a consumer’s choice constrained to a single time interval. In this problem, the choice is made over a set of perishable goods such that they do not retain value at the end of the period. Money has been introduced as the only means available to store that value for the future. Thus, consumer utility is measured on the possible combinations of goods consumed during the period and money held at the end of the period. Additionally, a set of simple conditions are assumed to the utility functions for goods and money given by: (1) Existence of a total utility that is additively separable with respect to the components of goods and money; (2) continuity of the derivatives of the utility functions of money and goods up to the second degree; and (3) non-uniqueness of the matrix obtained by differentiating the system of equations obtained by the condition of optimum. The article shows how the requirement of homogeneity conditions limits the possible expressions for the utility function of money. One of them is the frequently used logarithmic function.

Bector-Chandra Type Duality in Linear Programming Under Fuzzy Environment Using Hyperbolic Tangent Membership Functions

2019 ◽  
Vol 8 (2) ◽  
pp. 68-88
Author(s):  
Pratiksha Saxena ◽  
Ravi Jain
Keyword(s):  
Mathematical Model ◽  
Utility Function ◽  
Nonlinear Model ◽  
Probabilistic Approach ◽  
Utility Functions ◽  
Multi Objective Optimization ◽  
Total Utility ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives

Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. One approach to optimize a multi-objective mathematical model is to employ utility functions for the objectives. Recent studies on utility-based multi-objective optimization concentrates on considering just one utility function for each objective. But, in reality, it is not reasonable to have a unique utility function corresponding to each objective function. Here, a constrained multi-objective mathematical model is considered in which several utility functions are associated for each objective. All of these utility functions are uncertain and in fuzzy form, so a fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective. Meanwhile, the total utility function of the problem will be a fuzzy nonlinear mathematical model. Since there are not any conventional approaches to solve such a model, a defuzzification method to change the total utility function to a crisp nonlinear model is employed. Also, a maximum technique is applied to defuzzify the conditional utility functions. This action results in changing the total utility function to a crisp single objective nonlinear model and will simplify the optimization process of the total utility function. The effectiveness of the proposed approach is shown by solving a test problem.

EXISTENCE AND UNIQUENESS OF STEADY-STATE EQUILIBRIUM IN A GENERALIZED OVERLAPPING GENERATIONS MODEL

2011 ◽  
Vol 16 (S3) ◽  
pp. 299-311 ◽  
Author(s):  
Jinlu Li ◽  
Shuanglin Lin
Keyword(s):  
Steady State ◽  
Existence And Uniqueness ◽  
Overlapping Generations ◽  
Optimization Problem ◽  
Utility Functions ◽  
Overlapping Generations Model ◽  
State Equilibrium ◽  
Derivatives Of ◽  
Uniqueness Of Equilibrium ◽  
Diamond Type

Galor and Ryder [Journal of Economic Theory 49 (1989), 360–375] establish conditions for the existence of equilibrium in a Diamond-type overlapping-generations (OLG) model. Although theoretically appealing, these conditions are implicit and not convenient to apply. This paper provides explicit and easily applied conditions for the existence and uniqueness of steady-state equilibrium, with which one only needs to check the first derivatives of the production and utility functions and their interactions, with no need to solve the optimization problem. Our theorems on the existence and uniqueness of steady-state equilibrium can be applied to a larger class of OLG models that do not require second-order differentiability of the production and utility functions. We present examples to show how to check the existence and uniqueness of equilibrium.

Derivatives of Hadamard type in vector optimization

2018 ◽  
Vol 68 (2) ◽  
pp. 421-430
Author(s):  
Karel Pastor
Keyword(s):  
Nonlinear Analysis ◽  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimality Condition ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Dini Derivatives ◽  
Scalar Optimality ◽  
Derivatives Of

Abstract In our paper we will continue the comparison which was started by Vsevolod I. Ivanov [Nonlinear Analysis 125 (2015), 270–289], where he compared scalar optimality conditions stated in terms of Hadamard derivatives for arbitrary functions and those which was stated for ℓ-stable functions in terms of Dini derivatives. We will study the vector optimization problem and we show that also in this case the optimality condition stated in terms of Hadamard derivatives is more advantageous.

Modeling of Distributed Parameter Processes with Neural Networks

2014 ◽  
Vol 555 ◽  
pp. 530-540
Author(s):  
Honoriu Vălean ◽  
Mihail Abrudean ◽  
Mihaela Ligia Ungureşan ◽  
Iulia Clitan ◽  
Vlad Mureşan
Keyword(s):  
Neural Networks ◽  
Simulation Method ◽  
Distributed Parameter ◽  
Hearth Furnace ◽  
Original Solution ◽  
Steel Pipes ◽  
The Matrix ◽  
The Neural Networks ◽  
Derivatives Of ◽  
Seamless Steel

In this paper an original solution for the modeling of distributed parameter processes using neural networks is presented. The proposed method represents a particular alternative to a very accurate modeling-simulation method for this kind of processes, the method based on the matrix of partial derivatives of the state vector (Mpdx), associated with Taylor series. In order to compare the performances generated by the two methods, a distributed parameter thermal process associated to a rotary hearth furnace (R.H.F) from the technological flow of producing seamless steel pipes is considered. The main similarities and differences between the two methods are highlighted in the paper. The treated solution represents a premise for the usage of the neural networks in the automatic control of the distributed parameter processes domain.

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 1. Kinematic and stress states of the billet

2021 ◽  
pp. 65-71
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Complete System ◽  
Shape Change ◽  
Plane Deformation ◽  
System Of Equations ◽  
Flow Rates ◽  
Die Forging ◽  
The Matrix ◽  
Stress States ◽  
Theory Of Plastic Flow

On the basis of the complete system of equations of the theory of plastic flow, the kinematic and stress states of the billet are determined when the channels are extruded under conditions of plane deformation of the misaligned position of the punch and the matrix. Keywords: die forging, extrusion, misaligned position, punch, matrix, plane deformation, plastic flow rates, stresses. [email protected]

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 2. Determination of the extrusion force, maximum pressure on the matrix wall and the heights of the walls, taking into account the elastic deformation jf the matrix

2021 ◽  
pp. 63-69
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Elastic Deformation ◽  
Shape Change ◽  
Plane Deformation ◽  
Maximum Pressure ◽  
Extrusion Force ◽  
System Of Equations ◽  
The Matrix ◽  
Theory Of Plastic Flow

On the basis of the system of equations of the theory of plastic flow, the forces, the maximum pressure on the wall of the matrix and the heights of the obtained walls when extruding channels are determined, taking into account the elastic deformation of the matrix. Keywords: die forging, extrusion, misalignment, punch, matrix, plane deformation, stresses. [email protected]

DECISION ANALYSIS WITH MULTIPLE OBJECTIVES IN A FRAMEWORK FOR EVALUATING IMPRECISION

2005 ◽  
Vol 13 (05) ◽  
pp. 495-509 ◽  
Author(s):  
ARON LARSSON ◽  
JIM JOHANSSON ◽  
LOVE EKENBERG ◽  
MATS DANIELSON
Keyword(s):  
Decision Tree ◽  
Utility Function ◽  
Evaluation Method ◽  
Convex Sets ◽  
Utility Functions ◽  
Probability Measures ◽  
Decisions Under Risk ◽  
Closed Intervals ◽  
Pros And Cons ◽  
Tree Evaluation

We present a decision tree evaluation method for analyzing multi-attribute decisions under risk, where information is numerically imprecise. The approach extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise statements, relaxing requirements for precise estimates of decision parameters. Information is modeled in convex sets of utility and probability measures restricted by closed intervals. Evaluation is done relative to a set of rules, generalizing the concept of admissibility, computationally handled through optimization of aggregated utility functions. Pros and cons of two approaches, and tradeoffs in selecting a utility function, are discussed.

scholarly journals Residue-Residue Mutual Work Analysis of Retinal-Opsin Interaction in Rhodopsin: Implications for Protein-Ligand Binding

2019 ◽  
Author(s):  
Wenjin Li
Keyword(s):  
Virtual Work ◽  
Interaction Matrix ◽  
Time Interval ◽  
Transition Path ◽  
Transition Path Sampling ◽  
Decomposition Approach ◽  
Work Analysis ◽  
Nmr Study ◽  
The Matrix ◽  
Dynamics Simulations

AbstractEnergetic contributions at single-residue level to retinal-opsin interaction in rhodopsin were studied by combining molecular dynamics simulations, transition path sampling, and a newly developed energy decomposition approach. The virtual work at an infinitesimal time interval was decomposed into the work components on one residue due to its interaction with another residue, which were then averaged over the transition path ensemble along a proposed reaction coordinate. Such residue-residue mutual work analysis on 62 residues within the active center of rhodopsin resulted in a very sparse interaction matrix, which is generally not symmetric but anti-symmetric to some extent. 14 residues were identified to be major players in retinal relaxation, which is in excellent agreement with an existing NMR study. Based on the matrix of mutual work, a comprehensive network was constructed to provide detailed insights into the chromophore-protein interaction from a viewpoint of energy flow.

scholarly journals Comparing utility functions between risky and riskless choice in rhesus monkeys

2021 ◽  
Author(s):  
Philipe M. Bujold ◽  
Simone Ferrari-Toniolo ◽  
Leo Chi U Seak ◽  
Wolfram Schultz
Keyword(s):  
Utility Function ◽  
Utility Theory ◽  
Utility Maximization ◽  
Choice Behavior ◽  
Expected Utility Theory ◽  
Utility Functions ◽  
Random Utility Maximization ◽  
Risky Choices ◽  
Neuronal Mechanisms ◽  
Subjective Value

AbstractDecisions can be risky or riskless, depending on the outcomes of the choice. Expected Utility Theory describes risky choices as a utility maximization process: we choose the option with the highest subjective value (utility), which we compute considering both the option’s value and its associated risk. According to the random utility maximization framework, riskless choices could also be based on a utility measure. Neuronal mechanisms of utility-based choice may thus be common to both risky and riskless choices. This assumption would require the existence of a utility function that accounts for both risky and riskless decisions. Here, we investigated whether the choice behavior of macaque monkeys in riskless and risky decisions could be described by a common underlying utility function. We found that the utility functions elicited in the two choice scenarios were different from each other, even after taking into account the contribution of subjective probability weighting. Our results suggest that distinct utility representations exist for riskless and risky choices, which could reflect distinct neuronal representations of the utility quantities, or distinct brain mechanisms for risky and riskless choices. The different utility functions should be taken into account in neuronal investigations of utility-based choice.

scholarly journals Refinement Algoritm of Hypotheses Testing Research Based on Geochronological Tracking

2020 ◽  
Vol 6 (1) ◽  
pp. 86-93
Author(s):  
R. Ivakin ◽  
Y. Ivakin ◽  
S. Potapichev
Keyword(s):  
Spatial Data ◽  
Optimization Problem ◽  
Retrospective Studies ◽  
Subject Area ◽  
Statistical Testing ◽  
Time Interval ◽  
Data Sets ◽  
Hypotheses Testing ◽  
Practical Application ◽  
Spatial Data Sets

Geochronological tracking is an effective information technology for digital cartographic spatial data sets processing. It is widely known in retrospective patterns research about geographic relocation of figures, or any other units for a given time interval. Software component of geochronological tracking is becoming one the most popular GIS-integrated applications. The article presents the basic provisions for the algorithmization of the geochronological tracking procedure for statistical testing of retrospective studies hypotheses. We can observe the results of solving this optimization problem in a general form and in a number of the most typical variants. The obtained results of solving the optimization problem are interpreted in terms of the retrospective studies subject area. There are shown the ways of further practical application of the optimized algorithm in the tasks of modern logistics, data mining and formalized knowledge.

Sign in / Sign up

Export Citation Format

Share Document