Chapter 2 : Numerical optimization
. 1) Intro
2
↳
Solving tim
op problem
is a central
question in
eng. designs
exomple
morim profit ?
maxim
strength ?
which dimensions ?
?
weight
With set
of constraints
~
↳
* Some
histry
↳ optim started with Greek mathematician
-
problem solving by
Iove time
SEules and
Lage .
L
they min .
of a
body suly to
grovity between a points
2 1)
Design optimization process
.
↳ it'san iterative
process
Conventional
Design optim these
proces dingn changer
.
or
doe automatically ?
after running optim eng.
must c heck
din
a
~
it'
because
unlikely
volid and
Yields a
practicos design
Post-optimality doneto internet optimal designstudies
~ and trends
Where other
by performing design
-
param ,
vo I
quantify effect
and constraint !
parm .
varied
Are to in
objective
, . 3) Optimization problem
2
familation
L Home late their intent mathematical statement
design optim .
requires designer
to
variables Cxn xN ]
Design
-
X =
,
x2 .
…
…
Ls
↳
nx
denign variables,
y voluer in X =
Correspond to
design
~ Ses excomple loter on
xEIR
↳
If all element as continuu = Continuous problem
If 1 or more discrete = discrete
optim problem
.
with thickness certain t avail
.
↳ e .
sizing of camp. certain
,
only ar
f IR"-XIR Choice
-
objective function : -
of f is crucid ?
↳ we want to min f(x)
XE 1 Rm
un constrained
\
Constrained for x
e with
only
2
design .
var
umajcrity of
denign se
plr
sme
functions of denign .
var
↴
>
-
feasible region
equality constrain
=>
feasible set all Xt se that
{
comply hix =
inequality constraint
^
g(x)z0
~ inactive curtaint -
> then it could have been removed
#indep equality
.
const .
#design
vor -
(Mn = Mx)
otherwise
=> the problem becomes
wer constrained
니
can be - would
removed result ?
give
some
. 1) Intro
2
↳
Solving tim
op problem
is a central
question in
eng. designs
exomple
morim profit ?
maxim
strength ?
which dimensions ?
?
weight
With set
of constraints
~
↳
* Some
histry
↳ optim started with Greek mathematician
-
problem solving by
Iove time
SEules and
Lage .
L
they min .
of a
body suly to
grovity between a points
2 1)
Design optimization process
.
↳ it'san iterative
process
Conventional
Design optim these
proces dingn changer
.
or
doe automatically ?
after running optim eng.
must c heck
din
a
~
it'
because
unlikely
volid and
Yields a
practicos design
Post-optimality doneto internet optimal designstudies
~ and trends
Where other
by performing design
-
param ,
vo I
quantify effect
and constraint !
parm .
varied
Are to in
objective
, . 3) Optimization problem
2
familation
L Home late their intent mathematical statement
design optim .
requires designer
to
variables Cxn xN ]
Design
-
X =
,
x2 .
…
…
Ls
↳
nx
denign variables,
y voluer in X =
Correspond to
design
~ Ses excomple loter on
xEIR
↳
If all element as continuu = Continuous problem
If 1 or more discrete = discrete
optim problem
.
with thickness certain t avail
.
↳ e .
sizing of camp. certain
,
only ar
f IR"-XIR Choice
-
objective function : -
of f is crucid ?
↳ we want to min f(x)
XE 1 Rm
un constrained
\
Constrained for x
e with
only
2
design .
var
umajcrity of
denign se
plr
sme
functions of denign .
var
↴
>
-
feasible region
equality constrain
=>
feasible set all Xt se that
{
comply hix =
inequality constraint
^
g(x)z0
~ inactive curtaint -
> then it could have been removed
#indep equality
.
const .
#design
vor -
(Mn = Mx)
otherwise
=> the problem becomes
wer constrained
니
can be - would
removed result ?
give
some
