Veranstaltungen
Veranstaltungen der Fakultät für Mathematik
Approximation properties of Sum-Up Rounding, als osnao
Termin
29.11.2018, 14.15 Uhr - 15.15 Uhr
Veranstaltungsort
Mathematikgebäude, Raum M 511
Abstract
Partial outer convexication has been introduced as a relaxation technique for MINLPs
that are constrained by ordinary dierential equations. The family of Sum-Up Rounding
algorithms allows to approximate feasible points of the continuously-valued relaxation with
discrete ones that are feasible up to an arbitrarily small > 0. Advantageously, it does so in
linear time w.r.t the number of cells that make up the rounding grid.
Rening the rounding grid induces an improved approximation of the relaxed control
problem's trajectory in a suitable weak topology. If the dierential equation exhibits sucient
regularity, the corresponding sequence of state vectors can be shown to converge in norm.
We are able to prove the approximation property for ODEs and for time-dependent semilinear
PDEs under mild regularity assumptions on the solution trajectory of the PDE. In
particular, previous requirements of dierentiability and uniformly bounded derivatives on
the involved functions can be dropped.
Regarding PDE-Constrained MINLPs with integer variables distributed in more than one
dimension, we can combine an appropriate grid renement and a feasible ordering strategy
of the grid cells during the renements to employ a similar chain of arguments for a class of
elliptic PDE systems. We give a sucient condition for such desirable ordering strategies and
show that they are satised by the approximants of space-lling curves.
Vortragende(r)
M.Sc. Paul Manns
Herkunft der/des Vortragenden
TU Braunschweig
Approximation properties of Sum-Up Rounding, als osnao
Termin
29.11.2018, 14.15 Uhr - 15.15 Uhr
Veranstaltungsort
Mathematikgebäude, Raum M 511
Abstract
Partial outer convexication has been introduced as a relaxation technique for MINLPs
that are constrained by ordinary dierential equations. The family of Sum-Up Rounding
algorithms allows to approximate feasible points of the continuously-valued relaxation with
discrete ones that are feasible up to an arbitrarily small > 0. Advantageously, it does so in
linear time w.r.t the number of cells that make up the rounding grid.
Rening the rounding grid induces an improved approximation of the relaxed control
problem's trajectory in a suitable weak topology. If the dierential equation exhibits sucient
regularity, the corresponding sequence of state vectors can be shown to converge in norm.
We are able to prove the approximation property for ODEs and for time-dependent semilinear
PDEs under mild regularity assumptions on the solution trajectory of the PDE. In
particular, previous requirements of dierentiability and uniformly bounded derivatives on
the involved functions can be dropped.
Regarding PDE-Constrained MINLPs with integer variables distributed in more than one
dimension, we can combine an appropriate grid renement and a feasible ordering strategy
of the grid cells during the renements to employ a similar chain of arguments for a class of
elliptic PDE systems. We give a sucient condition for such desirable ordering strategies and
show that they are satised by the approximants of space-lling curves.
Vortragende(r)
M.Sc. Paul Manns
Herkunft der/des Vortragenden
TU Braunschweig