- 1 (388.93 KiB) Viewed 103 times
(1) Consider the following optimization problem min g(x1, ...,xn) subject to f1(x1, ...,xn) <an, f2(x1,...,xn) < az, མ ེ (3) fm (21, ..., 2n) sam, (4) (21, ..., Xn) EX CR”. (5) As an attempt to relax the above requirements (constraints), it is suggested to allow violation of some of the above constraints, subject to a constraint on the maximum number of violated constraints. For example, if the first two constraints are allowed to be violated, then the feasible space consists of con- straints 3, ..., m. However, the optimal choice of two violated constraints for minimization of g function is not known in advance. Therefore, 2 (1) Propose a mathematical programming model to minimize the function g, such that no more than any k out of the above m constraints are allowed to be violated. Hint: this mathematical programming model usually involves some big M coefficients. (2) If you employ the approach involving big M coefficients, provide a discussion of how the appropriate values of big M coefficients can be obtained.