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Multi-parametric Optimization and Control. Efstratios N. PistikopoulosЧитать онлайн книгу.

Multi-parametric Optimization and Control - Efstratios N. Pistikopoulos


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Equality Set Projection: A new algorithm for the projection of polytopes in halfspace representation. Technical Report CUED/F‐INFENG/TR.463. Cambridge University, Cambridge, UK.

      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.

      9 9 Schrijver, A. (1998) Theory of linear and integer programming, Wiley‐interscience series in discrete mathematics and optimization, Wiley, Chichester and New York.

      10 10 Bemporad, A. and Morari, M. (1999) Control of systems integrating logic, dynamics, and constraints. Automatica, 35 (3), 407–427, doi: 10.1016/S0005‐1098(98)00178‐2. URL http://www.sciencedirect.com/science/article/pii/S0005109898001782.

      11 11 Williams, H.P. (2013) Model building in mathematical programming, Wiley, Hoboken, NJ, 5th edn.

      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.

      Remark 2.1

      Note that it is possible to add a scalar images to the objective function of an LP problem without influencing the optimal solution. Similarly, it is possible to add an arbitrary scaling function images to an mp‐LP problem without influencing the optimal solution.

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      Remark 2.2

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