Michael Reichel (ari)
Es spricht Prof. Dr. Alexandra Schwartz (TU Dresden)
zum Thema: Continuous Reformulations of Cardinality-Constrained Problems: A Theoretical and Numerical Comparison
Abstract: Optimization problems that restrict the number of active variables arise in many modern applications — from feature selection in machine learning to sparse portfolio construction. The resulting ℓ0-sparsity term renders these problems discontinuous and nonconvex, placing them outside the reach of classical nonlinear optimization methods. Traditional remedies either introduce binary variables, yielding an equivalent mixed-integer formulation, or replace the ℓ0-sparsity term with an ℓ1-norm, resulting in a continuous but typically inexact surrogate problem.
A more recent approach reformulates these problems continuously by introducing auxiliary variables and complementarity-type constraints. This enables the use of nonlinear optimization techniques but calls for adapted stationarity concepts and specialized algorithms. This talk surveys several such reformulations, highlights their core ideas and theoretical differences, and illustrates their numerical performance.
Dienstag, 23. Juni 2026, 15:00 Uhr, Curie Hörsaal
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