1. DVIs are useful for representing models involving both dynamics and inequality constraints . 2. The SCOPF is bound by equality and inequality constraint limits. 3. Equality constraints can be replaced by two inequality constraints . 4. These added costs are used instead of the strict inequality constraints in the optimization. 5. One place where indirect methods have particular difficulty is on problems with path inequality constraints . 6. Introducing a slack variable replaces an inequality constraint with an equality constraint and a nonnegativity constraint. 7. The above quadratic program involves a very large, possibly infinite number of linear inequality constraints . 8. The method penalizes violations of inequality constraints using a Lagrange multiplier, which imposes a cost on violations. 9. G _ i and g _ j represent the inequality constraint functions at the upper and lower levels respectively. 10. The optima of problems with equality and / or inequality constraints can be found using the'Karush Kuhn Tucker conditions '.
