I used the KKT conditions to solve a convex optimization problem with 5 inequality constraints and 3 variables. I found 4 null Lagrangian multipliers and one non-null, function of one variable.
- How to interpret this situation?
- how to get the other 2 variables? Can I suppose equality for the other constraints.
If your objective function is $\ f(x,y)\ $, non-null Lagrange multiplier is $\ \lambda\ $, and constraint corresponding to $\ \lambda $ is $\ g(x,y)\ge 0\ $, then you should have $3$ equations \begin{align} \frac{\partial f}{\partial x}(x,y) - \lambda \frac{\partial g}{\partial x}(x,y)&=0\\ \frac{\partial f}{\partial y}(x,y) - \lambda \frac{\partial g}{\partial x}(x,y)&=0\\ g(x,y)&= 0 \end{align} to solve for the values of the three variables $\ x, y\ $, and $\ \lambda \ $ in an optimal solution.