In support vector machines, the minimization problem with inequality constraints can be converted to a minimization problem of Lagrange multipliers with equality constraints by KKT condition and Lagrange duality. The Lagrange multipliers have to be positive definite (or negative depending on the definition of the Lagrange multipliers).
How to solve this minimization problem of positive definite Lagrange multipliers with equality constraints? Maybe I can add additional Lagrange multipliers to get rid of the equality constraints, but how to deal with the fact that the original Lagrange multipliers are positive definite?
