There is a linear function of two variables that I am trying to minimize under an equality constraint. But, the constraint is non linear in the variables. Is there any technique to solve this? or can I use approximations and linearize the constraint?



Minimization under non-linear constraints
In addition to the tip about using Lagrange multipliers, take a look at <http://en.wikipedia.org/wiki/Nonlinear_programming> which has a small paragraph about methods for solving nonlinear optimization problems.


If you can know (or can show) that the problem is convex and you want to learn techniques for convex nonlinear optimization, take a look at the following textbook <http://www.stanford.edu/~boyd/cvxbook/> (pdf available)


