线性规划two-stageoptimizationproblem原题为minimizenorm(Ax+By+b,inf)withx属于R^ny属于R^pA,B,bareuncertainparameters.有m种可能的scenarios.inscenariok,A,B,b为Ak,Bk,bkFirst,selectxbeforethescenaroisknown;thenselec

Question

线性规划 two-stage optimization problem
原题为minimize norm(Ax+By+b,inf) with x属于R^n y属于R^p
A,B,b are uncertain parameters.有m种可能的scenarios.
in scenario k,A,B,b 为A_k,B_k,b_k
First,select x before the scenaro is known; then select y after learning the actual value of k.The optimal choice of y in the second stage is the value that minimizes ||A_k*x+B_k*y+b_k||inf for given x,A_k,B_k,b_k
* The dimensions of A,B,b are not given
Denote f_k(x) is the optimal value of this second-stage optimization problem of scenario k:
f_k(x)=min_y ||A_k*x+B_k*y+b_k||inf,k = 1,...,m.
=> the worst-case
minimize max_(from k=1,...,m) f_k(x) with x as variable
Formulate this as an LP
我的做法如下:
minimize t
subject to -u_k

Answer 1

我不是特别懂Linear Programming,不过你为什么要把u_k和v_k分开呢?
minimize t
subject to -t*ones(Nk,1)<=A_k*x+B_k*y+b_k<=t*ones(Nk,1) (k=1,...,m)
不过The dimensions of A,B,b are not given真不清楚是什么意思.