Nonlinear programming with discontinuous derivatives (DNLP)

Mathematically, the nonlinear programming with discontinuous derivatives (DNLP) problem looks like:

 L < x < U

where

x is a vector of variables that are continuous real numbers,

f(x) is the objective function,

α is a set of inequality and equality operators

g(x) represents the set of constraints

L and U are vectors of lower and upper bounds on the variables.

This is the same as NLP, except that non-smooth functions (abs, min, max) can appear in f(x) and g(x).  However one should note that the solvers may have problems when dealing with the discontinuities due to the fact that the solvers are really NLP solvers that are used on DNLPs and the optimality conditions plus the reliance on derivatives may be problematic.

Use of BARON, CBC and DICOPT may alleviate this problem.  For information on the names of the solvers that can be used on the DNLP problem class see the section on Solver Model type Capabilities.

Use of the model attribute TryLinear causes GAMS to see if the problem can be solved as a LP problem.