New PSG functions

New built-in functions extend the class of problems that can be solved with PSG.

New functions in PSG software

Recourse function (recourse_function) is a random convex function used for formulating, solving, and analyzing Two-Stage linear stochastic optimization problems. It is used as an argument of a Risk Function.

Sum of Splines Operator (spline_sum) calculates approximation splines. And can be used as argument of risk function in optimization problem and as a function with vector output in calculating.

Koenker and Basset Error (kb_err). Koenker and Bassett error of Linear Loss scenarios calculated with Matrix of Scenarios. Used for estimation of Value-at-Risk (i.e., percentile) in Linear Regression.

Rockafellar Error (ro_err) of Linear Loss scenarios is calculated with Matrix of Scenarios and used for estimation of Mixed Value-at-Risk in Linear Regression. Conditional Value-at-Risk approximately is equal to the discrete Mixed Value-at-Risk and can be estimated using  Rockafellar error in Linear Regression.

CVaR for Discrete Distribution as Function of Atom Probabilities (pcvar) is similar to the standard CVaR function, but decision variables are probabilities of scenarios.

CVaR for Mixture of Normal Distributions as Function of Mixture Weights (wcvar_ni) calculates CVaR for a mixture of normal distributions as a function of variable weights in this mixture.