As regards fuzzy mathematical programming: theory, application, and an extension are presented in [6].
Easy-to-use modeling languages coupled with powerful optimization solvers have greatly reduced the burden of implementation of mathematical programming theory into the practice of commercial network design.
Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel games, and mathematical programming theory itself.
Afterward, it was developed extensively by many researchers, which also included many interesting applications of this theory in different fields such as neural network theory, stability theory, mathematical programming, modeling theory, engineering sciences, medical sciences (medical genetics, nervous systems), image processing, control theory, communication, etc.
Several problem arising in different fields, such as mathematical programming, game theory, mechanics, and geometry, are to find solutions of the complementarity problems.
This umbrella concept of operational research covers many analytic approaches and methods, such as mathematical programming, queueing theory, simulation modeling, decision analysis, and forecasting methods.
Iterative algorithms have played a central role in the approximation solvability, especially of nonlinear variational inequalities as well as of nonlinear equations, in several fields such as applied mathematics, mathematical programming, mathematical finance, control theory and optimization, engineering sciences and others.
This problem is a fundamental problem in optimization theory, and it captures various applications such as partial differential equations, optimal control and mathematical programming; for the theory and application of VIs and related problems, the reader is referred, for example, to the works of Ceng et al. [1], Zegeye et al. [2], the papers of Yao et al. [3 5] and the many references therein.
The research on characterizations and generalizations of convexity and generalized convexity is one of the most important aspects in mathematical programming and optimization theory in [1 4].
Furthermore, we will show that many of these developments, which have a strong foundation in fundamentals of chemical engineering, numerical analysis, systems and control theory, mathematical programming, computer science and management science, have had significant impact in industry.
Now, we briefly recall some interesting works based on auction theory and mathematical programming.
