Condensed Information about the Test Problems

Abstract

To give a first survey of the test examples and their solution properties, we present a comprehensive list of all problems in Table 2. Beside the current problem number and the classification number OCD-Kr-s as described in Section 3 of Chapter I, we report the dimension n, the number of all inequality constraints m₁, the number of all equality constraints m-m₁, and the number of all bounds b. If linear restrictions exist, their number is given in the brackets behind m₁ or m-m₁, respectively. The column headed by x₀ gives the information, whether the starting point x₀ is feasible (T) or not (F). Some numerical data obtained by the analysis described in Section 2 of Chapter I are encluded. In particular, the objective function value f(x^*), the sum of constraint violations r(x^*), the norm of the Kuhn-Tucker-vector e(x^*), the number of active plus equality restrictions, i.e. $\overline {\rm \mu } :\, = \,{\rm \mu }\,{\rm + }\,{\rm m}\,{\rm - }\,{\rm m}_{\rm 1}$, the degree of degeneracy ${\rm u}_{\max }^* /{\rm u}_{{\rm min}}^{\rm *}$, and the condition number of the Hessian of the projected Lagrangian ${\rm \lambda }_{{\rm max}}^{\rm *} /{\rm \lambda }_{{\rm min}}^{\rm *}$ are listed. A value of 0. for ${\rm u}_{\max }^* /{\rm u}_{{\rm min}}^{\rm *}$ indicates that at least one multiplier ${\rm u}_{\rm j}^{\rm *}$ vanishes ($\left| {{\rm u}_{\rm j}^{\rm *} } \right|\, < \,.\,1{\rm E - 5}$) and that there are redundant constraints, i.e. the problem is degenerate. By ${\rm \lambda }_{{\rm max}}^{\rm *} /{\rm \lambda }_{{\rm min}}^{\rm *}$.