On the Regularization in J-Matrix Methods

The article is devoted to the issues of ensuring the competitiveness of a trading enterprise through its quantitative assessment. Analytic and graphical methods of evaluation are conventionally identified. The methodical approaches to the evaluation of the competitiveness of the trading enterprise, including the Rosenberg Model, the assessment of the quality level of production, matrix methods, the evaluation of comparative advantages, the multifactor score, the model of competitiveness are described, their strengths and weaknesses are identified.

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Optimizing Costs of Customer Attraction as a Competitiveness Factor

Vestnik of the Plekhanov Russian University of Economics ◽

10.21686/2413-2829-2019-6-172-182 ◽

2019 ◽

pp. 172-182

Author(s):

A. V. Katernyuk

Keyword(s):

Simplex Method ◽

Investment Analysis ◽

Economic Indicators ◽

The Internet ◽

Internet Services ◽

Induction Method ◽

Matrix Methods ◽

Fast Growing ◽

Analysis Methods ◽

Available Resources

In all spheres business experts try to raise competitiveness of the company by different ways, for instance at the expense of more efficient redistribution of available resources (costs). Objectives connected with modeling and optimizing resources used in advertising are becoming the most topical. Deeper knowledge in planning and conducting any marketing and advertising campaigns are in demand today among many specialists. The process of searching for and finding optimum costs of advertising in the Internet as a factor of the rise in the company sustainability can be successfully shaped through universal matrix methods of solution (e.g. simplex-method). Objectives which cannot be resolved by this method can be supplemented by such economic indicators, as profitability of investment and return on one ruble. The article summarizes the instrumental base dealing with estimating the efficiency of events connected with customer attraction to such a fast growing industry as internet-services. The author proposes besides traditional ways of expense optimization to take into account economic indicators connected with profitability of each sale channel. The following tools were used in the research: modeling, induction method, investment analysis, methods of statistics and formal logics, multi-criteria optimization, specific software meant for solving similar tasks, in particular special macros for excel table.

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On monotonicity and search strategies in face-based copositivity detection algorithms

Central European Journal of Operations Research ◽

10.1007/s10100-021-00737-6 ◽

2021 ◽

Author(s):

B. G.-Tóth ◽

E. M. T. Hendrix ◽

L. G. Casado

Keyword(s):

Research Question ◽

Quadratic Function ◽

Mixed Integer ◽

Quadratic Program ◽

Matrix Methods ◽

Detection Algorithms ◽

Standard Simplex ◽

Mathematical Properties ◽

The Face ◽

Spatial Branch And Bound

AbstractOver the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the relative interior minima of the standard quadratic program (StQP) and monotonicity. We derive several theoretical properties related to convexity and monotonicity of the standard quadratic function over faces of the standard simplex. We illustrate with numerical instances up to 28 dimensions the use of monotonicity in face-based algorithms. The question is what traversal through the face graph of the standard simplex is more appropriate for which matrix instance; top down or bottom up approaches. This depends on the level of the face graph where the minimum of StQP can be found, which is related to the density of the so-called convexity graph.

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Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v4i3.4052 ◽

2015 ◽

Vol 4 (3) ◽

pp. 420 ◽

Cited By ~ 1

Author(s):

Behrooz Basirat ◽

Mohammad Amin Shahdadi

Keyword(s):

Bernstein Polynomials ◽

Operational Matrix ◽

Numerical Procedure ◽

Operational Matrices ◽

Algebraic Equations ◽

Mixed Condition ◽

Matrix Methods ◽

Numerical Examples ◽

Linear Algebraic Equations ◽

The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

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