Hi, newe question, I had been using the basic Jayne Maximum Entropy Principle for choosing some probability distribution, P, subject to some equality constraints

{\displaystyle \sum _{i=1}^{n} P(x_{i})f_{k}(x_{i}) = F_{k}\qquad k=1,\ldots ,m.}

Now I need to generalize to inequality constraints.

{\displaystyle \sum _{i=1}^{n} P(x_{i})f_{k}(x_{i})\geq F_{k}\qquad k=1,\ldots ,m.}

I found this in wikipedia

In the case of inequality constraints, the Lagrange multipliers are determined from the solution of a convex optimization program with linear constraints. In both cases, there is no closed form solution, and the computation of the Lagrange multipliers usually requires numerical methods.

My current knowledge in the subject disallow me to find a source for how to do it that is clear to me.

I have checked a few (including the references of the wikipedia article) but everything is buried in the specific subject or application being solved.

It would be a great help if somebody point me to any basic material that explain how to state the `convex optimization program`

mentioned in the wikipedia article or something else.

Thank in advance