Engineering Optimization: Theory and Practice, Fourth Edition

1.8 Solution of Optimization Problems Using MATLAB 37

Table 1.2 MATLAB Programs or Functions for Solving Optimization Problems

Name of MATLAB program
Type of optimization Standard form for solution or function to solve
problem by MATLAB the problem

Function of one variable or
scalar minimization

Findxto minimizef (x)

withx 1 < x < x 2

fminbnd

Unconstrained minimization
of function of several
variables

Findxto minimizef (x) fminuncorfminsearch

Linear programming
problem

Findxto minimizefTx

subject to

[A]x≤b,[Aeq]x=beq,

l≤x≤u

linprog

Quadratic programming
problem

Findxto minimize

1

2 x

T[H]x+fTxsubject to

[A]x≤b,[Aeq]x=beq,

l≤x≤u

quadprog

Minimization of function of
several variables subject
to constraints

Findxto minimizef (x)

subject to

c(x)≤ 0 ,ceq= 0

[A]x≤b,[Aeq]x=beq,

l≤x≤u

fmincon

Goal attainment problem Findxandγto minimizeγ
such that
F (x)−wγ≤goal,
c(x)≤ 0 ,ceq= 0
[A]x≤b,[Aeq]x=beq,
l≤x≤u

fgoalattain

Minimax problem Minimize Max
x [Fi}

[Fi(x)}

such that

c(x)≤ 0 ,ceq= 0

[A]x≤b,[Aeq]x=beq,

l≤x≤u

fminimax

Binary integer programming
problem

Findxto minimizefTx

subject to

[A]x≤b,[Aeq]x=beq,

each component ofxis

binary

bintprog

g 2 (x 1 , x 2 )=

2500

π x 1 x 2

−

π^2 (x 12 +x 22 )

0. 5882

≤ 0

g 3 (x 1 , x 2 ) =−x 1 + 2 ≤ 0

g 4 (x 1 , x 2 )=x 1 − 41 ≤ 0

g 5 (x 1 , x 2 ) =−x 2 + 0. 2 ≤ 0

g 6 (x 1 , x 2 )=x 2 − 0. 8 ≤ 0