Dear Qianqian Wu,

The name CPLEX itself is a word game built on the concept of a simplex algorithm written in C. So C-Simplex trained CPLEX.

CPLEX has evolved over time to adopt and become a leader in linear programming categories, such as integer programming, mixed integer programming and quadratic programming.

For more details and information about this subject, i suggest you to see links and attached file on topic.

CPLEX Optimizer | IBM

https://www.ibm.com/analytics/cplex-optimizer

Linear_Programming - IBM Decision Optimization GitHub Catalog

https://ibmdecisionoptimization.github.io/.../Linear_Pro...

AIMMS :: CPLEX

https://www.aimms.com/english/.../solvers/cplex/

CPLEX 12 - GAMS

https://www.gams.com/26/docs/S_CPLEX.html

CPLEX 12 - GAMS

https://www.gams.com/26/docs/S_CPLEX.html

Best regards

CPLEX uses four main algorithms, Primal SImplex, Dual Simplex, Barrier Optimization methods for LPs. and the solution is globally optimal for LPs. For MIPs however, a relative gap to the best possible optimal value is given along withe the best solution CPLEX obtains using Branch and Cut