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