Techniques

Decomposition Techniques in Mathematical Programming: by Professor Antonio J. Conejo, Professor Enrique Castillo, Dr.

By Professor Antonio J. Conejo, Professor Enrique Castillo, Dr. Roberto Mínguez, Dr. Raquel García-Bertrand (auth.)

This textbook for college kids and practitioners offers a pragmatic method of decomposition options in optimization. It offers a suitable mixture of theoretical history and functional functions in engineering and technology, which makes the booklet attention-grabbing for practitioners, in addition to engineering, operations study and utilized economics graduate and postgraduate scholars. "Decomposition thoughts in Mathematical Programming" is predicated on clarifying, illustrative and computational examples and functions from electric, mechanical, power and civil engineering in addition to utilized arithmetic and economics. It addresses decomposition in linear programming, mixed-integer linear programming, nonlinear programming, and mixed-integer nonlinear programming, and gives rigorous decomposition algorithms in addition to heuristic ones. sensible functions are built as much as operating algorithms that may be effortlessly used. The theoretical history of the publication is deep adequate to be of curiosity to utilized mathematicians. It contains finish of bankruptcy routines and the options to the even numbered routines are integrated as an appendix.

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Extra resources for Decomposition Techniques in Mathematical Programming: Engineering and Science Applications

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M maximize dti , rti ; t = 1, 2, . . , m; i = 1, 2, . . , n z= n ki dti − et λt t=1 i=1 . 4 Energy Production Model Consider the triangular energy demand depicted in Fig. 6. In this figure, the vertical axis represents power and the horizontal axis time; therefore, the area Power d Energy 1 Time Fig. 6. Electricity demand curve for the energy production model 24 1 Motivating Examples Power 14 13 12 11 xi : Energy 10 p4 = 7 9 8 d=7 x4 = 6 1 14 5 4 x3 = p3 = 3 15 14 3 2 1 x2 = 10 7 p2 = 2 x 1 = 13/14 p1 = 1 1 Time Fig.

The amounts of energy produced by power plants 1 and 2 during period t are proportional to the corresponding water discharges during that period t. The proportionality constants for plants 1 and 2 are k1 and k2 , respectively. The river system is operated to supply the local electricity demand in each period, et . If additional energy can be produced during period t, it is sold at market price λt , with the objective of maximizing profits. Consider a time horizon of 2 h and assume that the reservoir contents at the beginning of the time horizon are r01 and r02 , for reservoirs 1 and 2, respectively.

The objective above is subject to the flow balance equations for all nodes (input amount of water equal to output amount of water including supplies and consumptions), ⎤ ⎡ x1 ⎤ ⎡ −q1 ⎤ ⎡ −1 −1 x2 −1 ⎢ q2 ⎥ x3 ⎥ ⎥⎢ ⎢ 1 ⎢ q3 ⎥ ⎥ 1 −1 −1 x ⎥⎢ ⎢ 4 ⎥ ⎢ ⎥ ⎥⎢ ⎢ 1 1 −1 ⎢ x5 ⎥ ⎢ q4 ⎥ ⎥ ⎢ x ⎢ ⎢ ⎥ ⎥ q 6 1 −1 5 ⎥ ⎢ x7 ⎥ ⎢ ⎢ ⎥ ⎢ x ⎥ ⎢ q6 ⎥ ⎢ 1 1 −1 ⎥ ⎢ 8 ⎥ = ⎢ q7 ⎥ ⎢ ⎥ . 1 1 1 ⎥ ⎢ x9 ⎥ ⎢ ⎢ ⎥ ⎢ x10 ⎥ ⎢ q8 ⎥ ⎢ −1 1 ⎥ ⎢ x11 ⎥ ⎢ q9 ⎥ ⎢ −1 1 1 ⎥ ⎥ x12 ⎥ ⎢ ⎢ −1 −1 1 ⎦⎢ q10 ⎥ ⎣ ⎣ ⎣ ⎦ ⎦ x 13 −1 1 q11 x14 −1 −1 −q12 x15 Note that both supply and consumption data qi (i = 1, .

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