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Solving mathematical programs with complementarity constraints by disjunctive regularizations
Sebastian Lämmel, Vladimir Shikhman
We propose a new disjunctive regularization for mathematical programs with complementarity constraints (MPCC). Its feasible set coincides with that of the Kanzow-Schwartz regulariz…
On stability of the Scholtes regularization for mathematical programs with complementarity constraints
Vladimir Shikhman, Sebastian Lämmel
For mathematical programs with complementarity constraints (MPCC), we study the stability properties of their Scholtes regularization. Our goal is to relate nondegenerate C-station…
Stationarity in nonsmooth optimization between geometrical motivation and topological relevance
Vladimir Shikhman
The goal of this paper is to compare alternative stationarity notions in structured nonsmooth optimization (SNO). Here, nonsmoothness is caused by complementarity, vanishing, ortho…
Scalarization via utility functions in multi-objective optimization
Lorenzo Lampariello, Simone Sagratella, Valerio Giuseppe Sasso +1
We study a general scalarization approach via utility functions in multi-objective optimization. It consists of maximizing utility which is obtained from the objectives' bargaining…
Optimality conditions for mathematical programs with orthogonality type constraints
Sebastian Lämmel, Vladimir Shikhman
We consider the class of mathematical programs with orthogonality type constraints (MPOC). Orthogonality type constraints appear by reformulating the sparsity constraint via auxili…
Critical point theory for sparse recovery
Sebastian Lämmel, Vladimir Shikhman
We study the problem of sparse recovery in the context of compressed sensing. This is to minimize the sensing error of linear measurements by sparse vectors with at most non-ze…