Minimization/ Maximization Necessary Conditions

1. Minimization Problem

If f(x) is quasiconvex, gi(x) is quasiconvex and hj(x) is affine (linear), then the necessary conditions are also sufficient conditions.

2. Maximization Problem

 If f(x) is quasiconcave, gi(x) is quasiconvex and hj(x) is affine (linear), then the necessary conditions are also sufficient conditions.

objective function: f(x)
inequality constraints: gi(x)≦0
equality constraints: hj(x)=0

符号に注意!!

http://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions

http://en.wikipedia.org/wiki/Convex_optimization