Laptin Y.P. – Institute of Cybernetics of
“Distorted" nonlinear programming Benchmarks – difficult ("deformed") test optimization
problems and a comparative analysis of software tools
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.