CVXPY
Minimize
  Sum(exp(x + [1. 2.]), None, False)
Subject To
 15: 1.0 <= x
Bounds
 x free
End
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AFTER COMPILATION
Either candidate conic solvers (['GUROBI']) do not support the cones output by the problem (ExpCone, NonNeg), or there are not enough constraints in the problem.
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GUROBI
Minimize
  exp_1[0] + exp_1[1]
Subject To
 15[0]: x[0] >= 1
 15[1]: x[1] >= 1
Bounds
 x[0] free
 x[1] free
 exp_1[0] free
 exp_1[1] free
General Constraints
\ exp_1[0] = exp(1 + x[0])
 GC0: exp_1[0] = NL : ( EXP , -1 , -1 ) ( PLUS , -1 , 0 ) 
  ( CONSTANT , 1 , 1 ) ( VARIABLE , x[0] , 1 )
\ exp_1[1] = exp(2 + x[1])
 GC1: exp_1[1] = NL : ( EXP , -1 , -1 ) ( PLUS , -1 , 0 ) 
  ( CONSTANT , 2 , 1 ) ( VARIABLE , x[1] , 1 )
End