By Antonio J. Conejo
This textbook for college kids and practitioners provides a pragmatic method of decomposition concepts in optimization. It presents a suitable mixture of theoretical history and functional functions in engineering and technological know-how, which makes the publication fascinating for practitioners, in addition to engineering, operations study and utilized economics graduate and postgraduate scholars. "Decomposition concepts in Mathematical Programming" relies on clarifying, illustrative and computational examples and functions from electric, mechanical, strength 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 purposes are built as much as operating algorithms that may be effortlessly used. The theoretical historical past of the booklet is deep sufficient to be of curiosity to utilized mathematicians. It contains finish of bankruptcy workouts and the recommendations of the even numbered workouts are integrated as an appendix.
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Additional resources for Decomposition techniques in mathematical programming
6 : relative “heights” or phases of nodes eij : electric energy ﬂowing through the line between nodes i and j. Variables x1 , x2 , y1 , y2 are nonnegative. , δ1 = 0. Constraints. 1. energy balance in every node (see Fig. 59) where eij = eij (δi , δj , Gij , Bij ) = Gij cos(δi − δj ) + Bij sin(δi − δj ) − Gij . 60) 44 1 Motivating Examples 2. 63) y2 ≤ y2max . 64) Function to Be Minimized. The nonlinear function to be minimized is the cost 2 i=1 1 axi xi + bxi x2i 2 2 + i=1 1 ayi yi + byi yi2 2 .
10. 11. 3 The Water Supply System Consider the water supply system in Fig. 11 consisting of two networks, the ﬁrst containing nodes 1 to 6, and the second nodes 7 to 12, connected by a single channel. Nodes 1 and 12 are assumed to be the water supply nodes and the rest are assumed to be consumption nodes with the ﬂow indicated by the q variables. Note that, in order to satisfy the balance equations, the values of the q variables must satisfy the constraint, q2 2 x1 x2 q3 x13 x3 q4 q9 4 x8 x6 x4 1 q1 q11 7 6 9 x15 x10 = 2 x7 3 q7 10 x9 q12 x14 q10 5 8 q5 12 x12 q6 x5 11 x11 q8 Fig.
Xn ci xi . 31) is called a facet . The feasibility region of this linear problem is denominated a polymatroid. Further details on polymatroids and their properties can be found in references [7, 8]. A relevant observation is that the solution of this production problem becomes nontrivial if additional linear constraints are imposed. For instance, if the joint energy production of devices 1 and 2 is required to be below 25 14 MWh, the merit order rule is no longer valid and the problem loses its polymatroid structure.