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Unformatted text preview: Edward Neuman Department of Mathematics Southern Illinois University at Carbondale edneuman@siu.edu This tutorial is devoted to the discussion of computational tools that are of interest in linear programming (LP). MATLAB powerful tools for computations with vectors and matrices make this package well suited for solving typical problems of linear programming. Topics discussed in this tutorial include the basic feasible solutions, extreme points and extreme directions of the constraint set, geometric solution of the linear programming problem, the TwoPhase Method, the Dual Simplex Algorithm, addition of a constraint and Gomory's cutting plane algorithm. ! Function Description abs Absolute value all True if all elements of a vector are nonzero any True if any element of a vector is nonzero axis Control axis scaling and appearance break Terminate execution of for or while loop clc Clear Command Window convhull Convex hull diff Difference and approximate derivative disp Display array eps Floating point relative accuracy eye Identity matrix find Find indices of nonzero of nonzero elements FontSize Size of a font gca Get handle to current axis get Get object properties grid Grid lines hold Hold current graph inf Infinity 2 intersect Set intersection isempty True for empty matrix length Length of vector LineStyle Style of a line LineWidth Width of a line max Largest component min Smallest component msgbox Message box nchoosek Binomial coefficient or all combinations patch Create patch pause Wait for user response plot Linear plot questdlg Question dialog box return Return to invoking function set Set object properties size Size of matrix sprintf Write formatted data to string sqrt Square root strcmp Compare strings sum Sum of elements title Graph title union Set union varargin Variable length input argument list varargout Variable length output argument list warning off Suppresses all subsequent warning messages xlabel Xaxis label ylabel Yaxis label zeros Zeros array To learn more about a particular MATLAB function type help functionname in the Command Window and next press the Enter key. " The following symbols will be used throughout the sequel. • n – ndimensional Euclidean vector space. Each member of this space is an ndimensional column vector. Lower case letters will denote members of this space. • m n – collection of all real matrices with m rows and n columns. Upper case letters will denote members of this space. • T – operator of transposition. In MATLAB the single quote operator ' is used to create transposition of a real vector or a real matrix. • x T y – the inner product (dot product) of x and y . • x – nonnegative vector. All components of x are greater than or equal to zero. 3 # $ % & ’ Some MATLAB functions that are presented in the subsequent sections of this tutorial make calls to functions named ver , delcols , MRT , MRTD and Br . These functions should be saved in the directory holding other mfiles that are used in this tutorial.directory holding other mfiles that are used in this tutorial....
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 Spring '97
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