Book chapter
Numerical Methods
Dynamics with Inequalities, pp.283-306
Other Titles in Applied Mathematics, Society for Industrial and Applied Mathematics
01/01/2011
DOI: 10.1137/1.9781611970715.ch8
Abstract
8.1 Choices
Numerical methods for dynamic problems with inequality constraints take several forms. The main families of methods are
• penalty methods, or the related index reduction methods,
• active set methods which track which inequality constraints are “active” (that is, where the inequalities are equalities), and
• time-stepping methods, in which for each time step, a CP or VI is solved.
Penalty methods aim to turn a nonsmooth or discontinuous differential equation into one that is smooth, and so we can use standard methods for differential equations. The true trajectory is often made up of smooth pieces joined by “kinks” or “jumps,” so active set methods aim to find the smooth pieces and the points at which a kink or jump occurs; once the kink or jump is reached, a new smooth differential equation is set up for the next piece. Time-stepping methods have the largest computational effort per time step, but they can be very effective when the active inequalities change frequently.
Details
- Title: Subtitle
- Numerical Methods
- Creators
- David E Stewart - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Dynamics with Inequalities, pp.283-306
- Series
- Other Titles in Applied Mathematics
- DOI
- 10.1137/1.9781611970715.ch8
- Publisher
- Society for Industrial and Applied Mathematics
- Language
- English
- Date published
- 01/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984242329302771
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