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Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints
TL;DR: An algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables that enforces descent on the objective function to promote global convergence to B-stationary points is proposed.
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Abstract: We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence.
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Citations
Finite Elements with Switch Detection for Direct Optimal Control of Nonsmooth Systems
Armin Nurkanovic,Mario Sperl,Sebastian Albrecht,Moritz Diehl +3 more
- 11 May 2022
TL;DR: The Finite Elements with Switch Detection (FESD) as mentioned in this paper is a numerical discretization method for nonsmooth differential equations, which is based on solving of nonlinear complementarity problems and able to automatically detect the non-smooth events in time.
FESD-J: Finite Elements with Switch Detection for Numerical Optimal Control of Rigid Bodies with Impacts and Coulomb Friction
Armin Nurkanovic,Jonathan Frey,Moritz Diehl +2 more
- 26 May 2023
TL;DR: In this paper , the authors extend the FESD method to the dynamic equations of multiple rigid bodies that exhibit state jumps due to impacts and Coulomb friction, referred to as FESDs with Jumps (FESD-J).
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