# Feasible direction

### From Glossary

Given a feasible point , a direction
vector, say , is feasible if there exists such that
is feasible. The *method of feasible directions* is designed
to choose a feasible direction at each iteration, along which (as
becomes positive) the objective value improves. Such directions
exist for continuous mathematical programs (where the line segment
is feasible for some ) unless
is a local optimum. (Note:
with nonlinear constraints, there is typically no feasible
direction according to this (classical) definition. See the
generalized reduced gradient method.)