Inequality constraint

Give definitions for the following maximum, minimum, optimum, unimodal, multimodal, local optimum, global optimum, continuous, discrete, constraint, equality constraint, inequality constraint, lower bound, upper bound, natural constraint, artificial constraint, degree of freedom, feasible region, nonfeasible region, factor tolerance. 

Inequality Constraints Inequality constraints on the future inputs or their rates of change are widely used in the MPC calculations. For example, if both upper and lower limits are required, the constraints could be expressed as... 

The combination of the equality constraints, inequality constraints, and lower and upper bounds defines a feasible region. A feasible solution is one that satisfies the equality constraints, the inequality constraints, and the upper and lower bounds for a feasible set of decision variables. If the solution also minimizes (or maximizes) the objective function, it is a local optimal solution. Sometimes, other local optimal solutions exist in the feasible region, with one or more being a global optimal solution. 

The simplest optimization problems are those without equality constraints, inequality constraints, and lower and upper bounds. They are referred to as unconstrained optimization. Otherwise, if one or more constraints apply, the problem is one in constrained optimization. 

We restrict ourselves to the case of equality constraints. Inequality constraints can be handled by the same techniques combined with an active set strategy [GMW81]. 

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