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Edward Neuman
Department of Mathematics
Southern Illinois University at Carbondale
[email protected]
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.
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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
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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.
¹ËÇ
"´³·³¶´»
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.
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 Spring '97
 glokgh
 Optimization, optimal solution, dual simplex algorithm, Simplex algorithm, legitimate variables

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