Month: December 2017

Sparse principal component analysis and its l1-relaxation

  • Santanu S. Dey
  • Rahul Mazumder
  • Marco Molinaro
  • Guanyi Wang
    • Categories (Mixed) Integer Nonlinear Programming, Data-Mining

    Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse, that is, we solve PCA with an additional cardinality (l0) constraint. The resulting optimization problem is called the sparse principal component … Read more

    Two-level value function approach to nonsmooth optimistic and pessimistic bilevel programs

  • Stephan Dempe
  • Boris S. Mordukhovich
  • Alain Zemkoho
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    The authors’ paper in Ref. [5], was the first one to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal value function introduced and analyzed in Ref. [4], for the case of optimistic bilevel programs. One of the basic assumptions in both of these … Read more