Affirmative Action Programs
30 Pages
English

Affirmative Action Programs

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Description

  • fiche de synthèse - matière potentielle : job announcements for distribution
WSDOT Equal Employment Opportunity and Affirmative Action Program 2007 – 2011 Fiscal Years Office of Equal Opportunity 310 Maple Park Avenue SE P.O. Box 47314 Olympia, WA 98504-7314
  • program progress on specific action items
  • occupational data
  • available labor pools of the communities
  • wsdot
  • affirmative plan executive summary
  • percent of the wsdot workforce to the percent of the available workforce
  • su
  • affirmative action plan
  • career development programs
  • workforce

Subjects

Informations

Published by
Reads 22
Language English
dohtemenalp-gnittuchpargipesdohtemenalp-gnittuccicepselcaroenalp-gnittucsmhtiroglanoitazilacol
methods
12.Cutting-plane
EE236C(Spring2010-11)
1-21
)ecitcarpdnayroehtni(tneiceeromhcumebnactubnahtpetsrepnoitatupmocdnayromemesmelborp)xevnocisauqdna(xevnocelbaitnereidnoneldnahpetshcaetasnoitcnuftniartsnocroevitcejbofotneidargbusenoeriuqerpetshcaetarellamssemocebhcihw,tesemosnitniopderisedezilacol
Localizationmethods
typicallyrequiremor subgradientmethod
-212
Cutting-planemethods
Cutting-planeoracle
n goal: findapointinconvexset C R ,ordeterminethat C isempty
n cutting-planeoracle: when queried at x R ,oracleeither
assertsthat x
returnsasepraaCti,ngrohyperplanebewtee
a T z b for z C,
oracleprovidesblack-boxdescriptionof C
Cutting-planemethods
nxandC:a
Tbxa
6=,0
13-2
Neutralanddeepcuts
neutralcut: a T x = b (querypointisonboundaryofhalfspacethatiscut)
deepcut: a T x>b (querypointisininteriorofhalfspacethatiscut)
Cutting-planemethods
C
x
C
x
214-
Unconstrainedminimization
takesetofminimizersof f as C
cutting-planeoracle (forconvex f ):if 0 6 = g ∂f ( x ) ,then
g T ( z x ) 0
definesa(neutral)cut ( a,b )=( g,g T x ) at x
proof: g T ( z x ) > 0 implies z 6∈ C because
Cutting-planemethods
f ( z ) f ( x )+ g T ( z x ) )x(f>
5-21
interpretation
levelcurvesof f
byevaluating g
f(x)ewruleo
x
ut
g
g T ( z x ) 0
halfspaceinserach
getone‘bit’ofinfo(onlocationof x )byevaluating g
Cutting-planemethods
frooptimum
6-21
Deepcutforunconstrainedminimization
supposeweknowanumber f ¯ with
f ( x ) >f ¯ f
( e.g. ,thesmallestvalueof f foundsofarinanalgorithm)
deepcut: if g
f(x),thenadeepcutisgivenb
g T ( z x )+ f ( x ) f ¯ 0
y
proof: f ( x )+ g T ( z x ) >f ¯ implies f ( z ) >f ,so z 6∈ C
Cutting-planemethods
7-21
Feasibilityproblem
C issolutionsetofconvexinequalities
cutting-planeoracle
f i ( x ) 0 ,i =1 ,...,m
if x notfeasible,find j with f j ( x ) > 0 andevaluate g j ∂f j ( x ) ;
isadeepcut
f j ( x )+ g jT ( z x ) 0
proof: f j ( x )+ g jT ( z x ) > 0 implies z 6∈ C because
Cutting-planemethods
f j ( z ) f j ( x )+ g jT ( z x ) > 0
8-21
Inequalityconstrainedproblem
C isthesetofoptimalpointsofconvexproblem
minimize f 0 ( x ) subjectto f i ( x ) 0 ,i =1 ,...,m
cutting-planeoracle
iiffxxiissnfoetasfiebale
fyas,elbisj
(x)>0,ewhave(deep)feasibili
f j ( x )+ g jT ( z x ) 0 where g j ∂f j ( x )
,ewhave(neutral)objectivecut
g 0 T ( z x ) 0 where g 0 ∂f 0 ( x )
ytcut
(or,deepcut g 0 T ( z x )+ f 0 ( x ) f ¯ 0 if f ¯ [ p ,f 0 ( x )) isknown)
Cutting-planemethods
19-2
(Conceptual)cutting-planealgorithm
given initialpolyhedron P 0 = { z | Az  b } knowntocontain C
repeat for k =1 , 2 ,... :
chooseapoint x ( k ) in P k 1 andquerythecutting-planeoracleat x ( k )
if x ( k ) C ,return x ( k )
else,addnewcutting-plane a kT z b k :
if P k =
,
Cutting-planemethods
quit
P k := P k 1 ∩{ z | a kT z b k }
01-21
geometry
P
k
giv
Pk1
esunce
Cutting-planemethods
rt
ak
)k(x
ainytofCafteriterationk
Pk
ak
)k(x
11-21