  Linear and nonlinear entanglement witnesses for a given bipartite quantum
systems are constructed. Using single particle feasible region, a way of
constructing effective entanglement witnesses for bipartite systems is provided
by exact convex optimization. Examples for some well known two qutrit quantum
systems show these entanglement witnesses in most cases, provide necessary and
sufficient conditions for separability of given bipartite system. Also this
method is applied to a class of bipartite qudit quantum systems with details
for d=3, 4 and 5. Keywords: non-linear and linear entanglement witnesses PACS
number(s): 03.67.Mn, 03.65.Ud
