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# ex-001-PCa.mod: Alternative Price-consistent NCP formulation of EPEC with 2 leaders
# 
# leader i's problem is:
#
#     minimize    (x_i+1)^2
#     subject to  s = x_1 + x_2 + y
#                 0 <= s  _|_  y >= 0
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set I := 1..2;

# ... leader variables
var x{I};

# ... follower variables
var s;
var y;

# ... multipliers
var lambda;
var sigma;
var nu;
var xi;

subject to 

	# ... first order conditions
	KKTx{i in I}: 2*(x[i]+1) + lambda = 0;
	KKTy:   lambda - nu    + xi*s = 0;
	KKTs: - lambda - sigma + xi*y = 0;

	slack: s = x[1] + x[2] + y   complements   lambda;
	bnds:  0 <= s     complements   sigma + y >= 0;
	bndy:  0 <= y     complements   nu + s >= 0;
	compl: 0 <= sigma + nu  complements   xi   >= 0;