Flippo, O.E. and Rinnoy Kan, A.H.G. Decomposition in general mathematical programming. Mathematical Programming, 60:361-382, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... c (k) c(x (k) where the generalized gradient (or subdi erential) is de ned as f(x) conv n g j g = lim i 1 rf(x i ) x i x; rf(x i ) exists converges o Problems of type (P ) arise as master problems in decomposition methods such as Benders Decomposition (e.g. 2] 10] and [9]) An important evolving area of application Numerical Analysis Report NA 195, Department of Mathematics, University of Dundee y Department of Mathematics, University of Dundee, DD1 4HN, U.K. fletcher maths.dundee.ac.uk, sleyffer maths.dundee.ac.uk 1 2 R. Fletcher and S. Ley er is in ....

Flippo, O.E. and Rinnoy Kan, A.H.G. Decomposition in general mathematical programming. Mathematical Programming, 60:361-382, 1993.

....is also relevant to bundle based decomposition schemes. Keywords: Nonlinear Programming, Benders Decomposition, Variable Decomposition, Bundle based Decomposition. 1 Introduction This note considers feasibility issues arising in Benders Decomposition (e.g. Geoffrion [5] or Flippo and Rinnoy Kan [3]) We are interested in Benders Decomposition as a mechanism for decomposing and solving large scale Nonlinear Programming (NLP) problems. An important and often difficult part in solving large NLP problems is to attain feasible points. This task is harder in Benders Decomposition as points must ....

....points. This task is harder in Benders Decomposition as points must be obtained which are feasible in the generated subproblems, whereas SQP methods for instance only require feasible QP approximations. In the remainder of this section Benders Decomposition is briefly reviewed (see [5] and [3] for a more detailed description) Consider the NLP problem (P ) 8 : minimize x;y f(x; y) subject to c(x; y) 0 (x; y) 2 X Theta Y; where the variables y are regarded as the complicating variables. In the context of decomposition, y are the linking variables and when y is fixed ....

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Flippo, O.E. and Rinnoy Kan, A.H.G. Decomposition in general mathematical programming. Mathematical Programming, 60:361--382, 1993.

....and Mixed Integer Linear Programming (MILP) problems. For instance, branch and bound [5] performs a tree search (integer part) solving an NLP problem at each node (nonlinear part) The decomposition is even more apparent in Outer Approximation ( 6] and [8] and Benders Decomposition ( 12] and [11]) where an alternating sequence of MILP master problems and NLP subproblems obtained by fixing the integer variables is solved. The recent branch and cut method for 0 1 convex MINLP of Stubbs and Mehrotra [23] also separates the nonlinear (lower bounding and cut generation) and integer part of the ....

Flippo, O.E. and Rinnoy Kan, A.H.G. Decomposition in general mathematical programming. Mathematical Programming, 60:361--382, 1993.

....selection and range reduction strategies. Generalized Benders decomposition [7] provides a different approach to solve BIL. It is studied in Geoffrion [18] Wolsey [35] Simoes [33] Flippo [13] Floudas and Visweswaran [15] 16] Visweswaran and Floudas [34] and Flippo and Rinnooy Kan [14]. QQP can also be written as a d.c. difference of convex) programming problem in which the objective function is linear and each function Q k is expressed as a d.c. function. Phong, Tao and Hoai An [24] presents an outer approximation method for such problems. 2.2 Initial Relaxation The ....

FLIPPO O.E. and RINNOOY KAN A.H.G.(1993), "Decomposition in General Mathematical Programming," Mathematical Programming 60, 361--382.

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