15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, 12 — 14 juillet 2017

15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, 12 — 14 juillet 2017

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Variational Analysis and Nonsmooth Optimization I

12 juil. 2017 11h30 – 12h45

Salle: Amphithéâtre Banque Nationale

Présidée par Tim Hoheisel

3 présentations

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    11h30 - 11h55

    Convergence of a Scholtes-Type Relaxation Method for Optimization Problems with Cardinality Constraints

    • Alexandra Schwartz, prés., TU Darmstadt
    • Martin Branda, Charles University Prague
    • Max Bucher, TU Darmstadt
    • Michal Cervinka, Charles University, Prague

    Optimization problems with cardinality constraints have applications for example in portfolio optimization. However, due to the discrete-valued cardinality constraint, they are not easy to solve. We provide a continuous reformulation of cardinality constraints and discuss the convergence of a Scholtes-type relaxation method for the resulting nonlinear programs with orthogonality constraints. Furthermore, we show preliminary numerical results for portfolio optimization problems with different risk measures.

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    11h55 - 12h20

    Convex analysis of the generalized matrix-fractional function

    • Tim Hoheisel, prés., McGill University

    We study the support functional of a graph of a matrix-valued mapping intersected with an affine manifold. This support function establishes a connection between optimal value functions for quadratic optimization problems, the matrix-fractional function, the pseudo matrix-fractional function, the nuclear norm, and multi-task learning. As a core result we present a new and elegant description of the closed convex hull of the supported set which opens the door for various applications, many of which will be presented in the talk.

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    12h20 - 12h45

    Stability of minimizers of set optimization problems

    • Michel GEOFFROY, prés., Université des Antilles (LAMIA)

    We investigate, in a unified way, the stability of several relaxed minimizers of set optimization problems.
    To this end, we introduce a topology on vector ordered spaces from which we derive a concept of convergence that allows us to study both the upper and the lower stability of the sets of relaxed minimizers we consider.