This theory provides us with a framework to understand and solve many problems arising in the field of economics, optimization, transportation, elasticity and applied sciences.
The variational inequality theory, which is mainly due to Stampacchia [1], provides very powerful techniques for studying problems arising in mechanics, optimization, transportation, economics, contact problems in elasticity, and other branches of mathematics.
Numerous problems in physics, optimization, transportation, signal processing, and economics are reduced to find a solution to equilibrium problems, which cover fixed point problems, variational inequalities, saddle problems, inclusion problems, and so on.
A famous example of an NP-complete problem is the traveling salesman problem, which has wide applications in the optimization of transportation schedules.
His research interests include optimization, logistics, transportation modeling, multiobjective optimization, heuristics and combinatorial optimization.
The equilibrium problem (1.1) includes as special cases numerous problems in physics, optimization, economics, transportation, and engineering.
The mixed equilibrium problem (MEP) includes several important problems arising in physics, engineering, science optimization, economics, transportation, network and structural analysis, Nash equilibrium problems in noncooperative games and others.
The equilibrium problem is an unifying model for several problems arising in physics, engineering, science optimization, economics, transportation, network and structural analysis, Nash equilibrium problems in noncooperative games, and others.
The mixed equilibrium problem (MEP) includes serval important problems arising in physics, engineering, science optimization, economics, transportation, network and structural analysis, Nash equilibrium problems in noncooperative games and others.
Still, optimization of transportation supply under equilibrium assumption may not guarantee that an effective solution is obtained; indeed the system may not evolve towards the equilibrium state, if this state is not stable.
Variational inequality theory has appeared as an effective and powerful tool to study and investigate a wide class of problems arising in pure and applied sciences including elasticity, optimization, economics, transportation, and structural analysis; see, for instance, [1 4] and the references therein.
