Linear Programming, Nonlinear Programming, Nonlinear Equations, and Nonlinear Regression Using Solver

2013 ◽  
pp. 197-212
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Nonlinear Equations ◽  
Nonlinear Regression

Minimax Input Shaper Design Using Linear Programming

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Tarunraj Singh
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Barycentric Coordinates ◽  
Nonlinear Programming Problem ◽  
Dome A ◽  
Input Shaper ◽  
Maximum Value ◽  
The Cost

The focus of this paper is on the design of robust input shapers where the maximum value of the cost function over the domain of uncertainty is minimized. This nonlinear programming problem is reformulated as a linear programming problem by approximating a n-dimensional hypersphere with multiple hyperplanes (as in a geodesic dome). A recursive technique to approximate a hypersphere to any level of accuracy is developed using barycentric coordinates. The proposed technique is illustrated on the spring-mass-dashpot and the benchmark floating oscillator problem undergoing a rest-to-rest maneuver. It is shown that the results of the linear programming problem are nearly identical to that of the nonlinear programming problem.

Application of a New Penalty Function Method to Design Optimization

1977 ◽  
Vol 99 (1) ◽  
pp. 31-36 ◽  
Author(s):  
S. B. Schuldt ◽  
G. A. Gabriele ◽  
R. R. Root ◽  
E. Sandgren ◽  
K. M. Ragsdell
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Design Optimization ◽  
Penalty Function ◽  
Function Method ◽  
Test Problems ◽  
Penalty Function Method ◽  
Method Of Multipliers ◽  
Non Linear Programming ◽  
Linear Programming Problems

This paper presents Schuldt’s Method of Multipliers for nonlinear programming problems. The basics of this new exterior penalty function method are discussed with emphasis upon the ease of implementation. The merit of the technique for medium to large non-linear programming problems is evaluated, and demonstrated using the Eason and Fenton test problems.

Kapees3: A High-Quality VLSI Placement Tool Using Nesterov’s Method for Density Penalty

2018 ◽  
Vol 27 (08) ◽  
pp. 1850122
Author(s):  
Sameer Pawanekar ◽  
Kalpesh Kapoor ◽  
Gaurav Trivedi
Keyword(s):  
Nonlinear Programming ◽  
Nonlinear Equations ◽  
Analytical Approach ◽  
Quadratic Optimization ◽  
Experimental Results ◽  
Standard Cell ◽  
Feng Shui ◽  
High Quality ◽  
Cell Placement ◽  
Number Of Cells

We present an analytical approach that is based on nonlinear programming to perform VLSI standard cell placement. Our method first clusters a netlist to reduce the number of cells and then performs quadratic optimization on the reduced netlist. Finally, it uses Nesterov’s method for solving nonlinear equations for the problem. The framework of our tool, Kapees3, is scalable and generates high quality results. The experimental results for Peko Suite 1 and Peko Suite 2 benchmarks show promising improvements. Our placement tool outperforms NTUPlace3, Dragon, Feng Shui, Capo10.5, by 46%, 57%, 48% and 25%, respectively, on PEKO Suite 1. For PEKO Suite 2, our placement tool outperforms NTUPlace3, Dragon, Feng Shui, Capo10.5 and mPL6 by 30%, 47%, 57%, 69% and 2.7%, respectively. On MMS benchmarks, we obtain wirelength improvement over Capo10.5 by 56.62%, FLOP by 7.84%, FastPlace by 11.55%, ComPLx by 4.58%, POLAR by 23.67%, mPL6 by 9.96% and NTUPlace3-Unified by 2.96%.

scholarly journals On Some Aspects of the Examination in Econometrics

2021 ◽  
Vol 8 (3) ◽  
pp. 7-16
Author(s):  
Symon Serbenyuk
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Mathematical Models ◽  
Mathematical Optimization ◽  
Input Output ◽  
High Quality ◽  
Mathematical Economics ◽  
Linear And Nonlinear Programming ◽  
Scientific Results ◽  
Method Of Lagrange Multipliers

Teaching econometrics has been studied by a number of researchers, however, there is little information available on the quality of examination and on simplification of tests for demonstration the high-quality knowledge by students in concrete topics of econometrics or mathematical economics.One can note the following main goals of studying the basics of mathematical economics or econometrics by students: forming the notions of mathematical model and of modeling economic processes and phenomena; understanding a role of using mathematical models for economics research and obtaining scientific results; formatting skills for constructing mathematical models in economics, for solving economics problems by mathematical modeling.The main goal of this paper is to simplify test tasks, is to help to students to demonstrate the high-quality knowledge in certain areas of mathematical economics, and also is to construct a system of testing tasks, in which the emphasis was placed on the knowledge and understanding of an algorithm of solving the problem.In the present paper, to quality examine the student knowledge in the basics of mathematical economics, a certain system of tests was constructed and is considered. The main attention is also given to algorithms and techniques of solving some tasks (problems) of mathematical economics. The following topics of mathematical economics are viewed: constructing mathematical models of linear programming, the input-output model, the Monge-Kantorovich transportation problem, the simplex method of linear programming, the graphic method of linear and nonlinear programming, the method of Lagrange multipliers in mathematical optimization. Some primary basic results of studying linear programming, nonlinear programming, and the input-output model are noted.A new system of tests that satisfies the aim of this paper is modeled. The described tests require less time for solving than usual tasks. Here we do not focus on the repetition of auxiliary mathematical knowledge and arithmetic skills. These tests are simplified versions of standard tasks and help students to demonstrate knowledge in the mentioned topics of mathematical economics. The tasks are focused only on the knowledge of basic formulas, techniques, and connections between mathematical objects, economic systems, and their elements.

scholarly journals Laplace Distribution And Probabilistic (bi) In Linear Programming Model

2011 ◽  
Vol 17 (61) ◽  
pp. 20
Author(s):  
Ali Khaleel Al-zubidi
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Programming Model ◽  
Random Variable ◽  
Laplace Distribution ◽  
Probabilistic Programming ◽  
Economic Agents ◽  
Specification Errors ◽  
Nonlinear Programming Model

The theory of probabilistic programming  may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, pro­duction and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient bi is random variable with given Laplace distribution.

Computer Models in Advertising Media Selection

1968 ◽  
Vol 5 (4) ◽  
pp. 414-424 ◽  
Author(s):  
Dennis H. Gensch
Keyword(s):  
Dynamic Programming ◽  
Linear Programming ◽  
Nonlinear Programming ◽  
Computer Models ◽  
Media Selection ◽  
Marginal Analysis ◽  
Heuristic Programming

There is a clear dichotomy between the optimizing and the nonoptimizing approaches. The four main methods using the optimizing approach are: (1) linear programming, (2) nonlinear programming, (3) iteration or marginal analysis, and (4) dynamic programming. The two major nonoptimizing approaches are (1) heuristic programming and (2) simulation. One of the known models using each approach is examined in detail. The relative merits of the various approaches are then discussed.

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