Review
For convex opt problem CP't value of primalp main fCH st gift to kick C
KKT conditions are1 gifx't c 0 for kick2 I 20 for keek3 X CilgiCx O for kick4 Of It lil Ogi 1 0
yard differentiable
Thin It f g ge are convex and X't I satisfy 1 4then X't is optimal If the gi are linear or
if exists strictly feasible to gf.to to failthen there exist and that satisfy 1 y
Can we replace g ge with
GCA moat gift
G CHEO girl EO tiG is convex because mat of comet is concrete
Max is not differentiable Xmae cx.ir at 4,4f CholmatGestly
HE s 0
I sco
If had match sat GCHEO
min CH St gekko kick
Lagrange LG D felt Exilgia9CH int LAHd't Max ECD
420
lend a CH E f H AKO feasible x weakdualitySo d E p'tproof t feasible gift e O e tiX zo Evil gift O
had fat ExilgiH Eff
9CH iff Lao xa 4x4
9 CH e fat
9 H int LK H int can give A
no constraints on
ME HH ACH concave
LG X for every x is linear andinf of linearfees is concave
Thani stroy dualityIf f g gd are differentiable convexand either g gd are linear or strictly feasiblethen d p
