Sebastian Lämmel, Vladimir Shikhman, On mathematical programs with sign constraints and their applications in regularization theory
Full Text: PDF
DOI: 10.23952/jnva.10.2026.2.6
Volume 10, Issue 2, 1 April 2026, Pages 343-361
Abstract. We study a novel class of nonsmooth optimization problems, called mathematical programs with sign constraints (MPSiC). For MPSiC, the critical point theory is developed. It includes the introduction of topologically relevant T-stationary points along with their T-index. Two typical results within the scope of Morse theory are demonstrated. Outside the set of T-stationary points, the MPSiC lower level sets remain homotopy-equivalent. If surpassing a nondegenerate T-stationary point, a cell of dimension equal to its T-index has to be attached for this purpose. Further, we apply our findings on the MPSiC class to the sign-type regularization of mathematical programs with complementarity constraints (MPCC) from [A. Kadrani, J.P. Dussault, A. Benchakroun, A new regularization scheme for mathematical programs with complementarity constraints, SIAM J. Optim. 20 (2009), 78–103]. By doing so, the convergence analysis for the sign-type regularization of MPCC is refined. Among the other results, an index shift for limiting C-stationary points of MPCC can not be avoided in the generic sense. In particular, a sequence of saddle points of the sign-type regularization might converge to a minimizer of MPCC. This phenomenon turns out to be stable with respect to 
How to Cite this Article:
S. Lämmel, V. Shikhman, On mathematical programs with sign constraints and their applications in regularization theory, J. Nonlinear Var. Anal. 10 (2026), 343-361.