epäyhtäläisehtojen

Epäyhtäläisehtojen is a Finnish term that refers to inequality conditions used in mathematical problems, particularly in optimization, economics, and operations research. The word is derived from “epäyhtäläiset ehdot”, which literally means “inequality conditions” where “epäyhtäläiset” translates to “inequalities” and “ehdot” to “conditions”. Inequality constraints are a fundamental component of linear programming (LP) and integer programming (IP) models, as well as in nonlinear optimization formulations such as quadratic programming and convex optimization.

In an optimization model, equality constraints fix a linear combination of variables to an exact value, whereas inequality constraints restrict the variable space to one side of a hyperplane. A typical linear inequality takes the form ax ≤ b or ax ≥ b, where a is a vector of coefficients, x the vector of decision variables, and b a real number. These constraints define a feasible region that is a convex polyhedron when only linear inequalities are present. In the presence of integer decision variables, the feasible region becomes a discrete set of integer points within that polyhedron.

Inequality constraints are used to encode capacity limits, resource budgets, risk thresholds, and policy requirements in mathematical programs. They also play a key role in sensitivity analysis, duality theory, and in the formulation of robust optimization problems, where bounds on uncertainties are modeled as inequalities.