The Benders Subproblem is as follows:
The decision variables:\alpha_t, \beta_t,r_{it},m_i,and others are known parameters.
Soving the problem by Python+gurobi ,the output is as follows:
Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (win64)
Optimize a model with 45 rows, 58 columns and 126 nonzeros
Model fingerprint: 0xc76df5b0
Coefficient statistics:
Matrix range [9e-01, 2e+02]
Objective range [1e+00, 2e+03]
Bounds range [0e+00, 0e+00]
RHS range [5e-01, 8e-01]
Presolve removed 45 rows and 58 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Iteration Objective Primal Inf. Dual Inf. Time
0 1.2182075e+04 0.000000e+00 0.000000e+00 0s
Solved in 0 iterations and 0.01 seconds
Optimal objective 1.218207529e+04
Where Model.satus=2,which means the optimal solution is available. The optimal objective is equal to 12182.The problem is bounded.
Soving the problem by Matlab+cvx+mosek ,the output is as follows:
Calling Mosek 9.1.9: 115 variables, 50 equality constraints
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : LO (linear optimization problem)
Constraints : 50
Cones : 0
Scalar variables : 115
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 0 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Optimizer terminated. Time: 0.13
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.6005008384e+03 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00
Basic solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.6005008384e+03 nrm: 2e+02 Viol. con: 0e+00 var: 0e+00
Optimizer summary
Optimizer - time: 0.13
Interior-point - iterations : 0 time: 0.05
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Status: Unbounded
Optimal value (cvx_optval): +Inf
Where the cvx_status=unbounded, which means the optimal solution doesn’t exist.
Question: The results obtained by the two solvers are different. And we guess whether it is caused by cvx?