Multi-parametric Optimization and Control. Efstratios N. Pistikopoulos
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Название: Multi-parametric Optimization and Control
Автор: Efstratios N. Pistikopoulos
Издательство: John Wiley & Sons Limited
Жанр: Математика
isbn: 9781119265191
isbn:
(1.37d)
where
(1.38)
1.4 Organization of the Book
The remainder of this book is organized in two parts. In the first part, the theoretical and algorithmic essentials of multi‐parametric programming problems will be established. These include algorithms for the solution of multi‐parametric linear programming (mp‐LP), multi‐parametric quadratic programming (mp‐QP), multi‐parametric mixed‐integer linear programming (mp‐MILP), and multi‐parametric mixed‐integer quadratic programming (mp‐MIQP) problems. On the other hand, the latter of these parts is focused on the applications of multi‐parametric programming and specifically on its utilization to provide solutions to receding horizon optimization problems such as model predictive control.
References
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8 8 Kouramas, K.I., Panos, C., Faísca, N.P., and Pistikopoulos, E.N. (2013) An algorithm for robust explicit/multi‐parametric model predictive control. Automatica, 49 (2), 381–389, doi: 10.1016/j.automatica.2012.11.035. URL http://www.sciencedirect.com/science/article/pii/S0005109812005717.
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11 11 Williams, H.P. (2013) Model building in mathematical programming, Wiley, Hoboken, NJ, 5th edn.
Notes
1 1 A function is called pseudo‐convex if for all feasible where we have .
2 2 A function is called quasi‐convex if for all feasible and we have . Note that a quasi‐concave function is a function whose negative is quasi‐convex.
2 Multi‐parametric Linear Programming
Consider the following linear programming (LP) problem:
where
where