** Laptin Y.P. **–

*“Distorted" nonlinear programming Benchmarks** – ***d****ifficult**** (**"deformed"**) test optimization
problems and a comparative analysis of software tools**

description of family problems | AMPL description of problems, the results
of calculations

The family of optimization
problems with constraints, the degree of degeneracy depends on the
parameters. It is formed from a set of basic problems by multiplying the
inequalities of the constraints of the problems by strictly positive smooth
functions (feasible sets of problems are not changed). Due to such
transformation the scale degeneracy is reached in the optimal
point. Another class of problems is generated by multiplying the
inequalities by a strictly positive oscillatory function. Penalty functions of
these problems are multiextremal, what is difficult to overcome with
conventional optimization techniques.

This family of optimization problems was designed to demonstrate the advantage of the convex
conical extensions method for solving optimization problems with
constraints.

All test problems are implemented in AMPL language (http://www.ampl.com/index.html), the
prepared files are ready for AMPL environment. The files contain commands
of AMPL to organize a series of runs for different solvers. Runs are made for
different values of the parameters determining poor conditioning of the
problems. Parameters are chosen so that these solvers do not cope with
these problems. Results of computational experiments are presented.