integerfeasible

Integerfeasible refers to a property of a solution or a point within a mathematical problem, particularly in the field of optimization. A solution is considered integerfeasible if all of its variables take on integer values. This is a crucial distinction in integer programming problems, where the objective is to find an optimal solution that not only satisfies certain constraints but also consists solely of integers.

For example, in a problem involving the production of discrete items, such as cars or chairs, the number of items produced must be a whole number. A solution suggesting the production of 10.5 cars would not be integerfeasible. The constraints of the problem, such as resource availability or demand, must also be met by this integer solution.

The process of finding an integerfeasible solution can be significantly more complex than finding a general real-valued solution. Algorithms designed for integer programming, such as branch and bound or cutting plane methods, are employed to systematically search for optimal integer solutions. The existence and nature of integerfeasible solutions are fundamental concepts in understanding and solving integer optimization problems across various domains, including logistics, finance, and operations research.