Magnus Önnheim
Chalmers University of Technology
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Featured researches published by Magnus Önnheim.
Mathematical Programming | 2017
Magnus Önnheim; Emil Gustavsson; Ann-Brith Strömberg; Michael Patriksson; Torbjörn Larsson
Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? We answer this question in the affirmative for a convex program and an associated subgradient algorithm for its Lagrange dual. We show that the primal–dual pair of programs corresponding to an associated homogeneous dual function is in turn associated with a saddle-point problem, in which—in the inconsistent case—the primal part amounts to finding a solution in the primal space such that the Euclidean norm of the infeasibility in the relaxed constraints is minimized; the dual part amounts to identifying a feasible steepest ascent direction for the Lagrangian dual function. We present convergence results for a conditional
Journal of Geometric Analysis | 2018
Jakob Hultgren; Magnus Önnheim
Computers & Industrial Engineering | 2014
Emil Gustavsson; Michael Patriksson; Ann-Brith Strömberg; Adam Wojciechowski; Magnus Önnheim
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Mathematical Methods of Operations Research | 2012
Torgny Almgren; Niclas Andréasson; Michael Patriksson; Ann-Brith Strömberg; Adam Wojciechowski; Magnus Önnheim
Analysis & PDE | 2018
Robert J. Berman; Magnus Önnheim
ε-subgradient optimization algorithm applied to the Lagrangian dual problem, and the construction of an ergodic sequence of primal subproblem solutions; this composite algorithm yields convergence of the primal–dual sequence to the set of saddle-points of the associated homogeneous Lagrangian function; for linear programs, convergence to the subset in which the primal objective is at minimum is also achieved.
Proceedings of 4th Production and Operations Management World Conference, July 2012 | 2012
Torgny Almgren; Niclas Andréasson; Myrna Palmgren; Michael Patriksson; Ann-Brith Strömberg; Adam Wojciechowski; Magnus Önnheim
In this paper we consider Monge–Ampère equations on compact Hessian manifolds, or equivalently Monge–Ampère equations on certain unbounded convex domains in Euclidean space, with a periodicity constraint given by the action of an affine group. In the case where the affine group action is volume preserving, i.e., when the manifold is special, the solvability of the corresponding Monge–Ampère equation was first established by Cheng and Yau using the continuity method. In the general case we set up a variational framework involving certain dual manifolds and a generalization of the classical Legendre transform. We give existence and uniqueness results and elaborate on connections to optimal transport and quasi-periodic tilings of convex domains.
arXiv: Mathematical Physics | 2016
Robert J. Berman; Magnus Önnheim
Archive | 2013
Michael Patriksson; Niclas Andréasson; Anton Evgrafov; Emil Gustavsson; Magnus Önnheim
Archive | 2016
Niclas Andréasson; Anton Evgrafov; Michael Patriksson; Emil Gustavsson; Zuzana Nedelkova; Kin Cheong Sou; Magnus Önnheim
Archive | 2013
Magnus Önnheim