xact penalty methods form an important class of methods for solving constrained optimization problems. Using penalty functions, the original constrained optimization problem can be transformed in an “equivalent” unconstrained problem. In this chapter we show how grossone can be utilized in constructing exact differentiable penalty functions for the case of only equality constraints, the general case of equality and inequality constraints, and quadratic problems. These new penalty functions allow to recover the solution of the unconstrained problem from the finite term (in its grossone expansion) of the optimal solution of the unconstrained problem. Moreover, Lagrangian duals associated to the constraints are also automatically obtained from the infinitesimal terms. Finally a new algorithmic scheme is presented.
The Role of grossone in Nonlinear Programming and Exact Penalty Methods
De Leone, Renato
2022-01-01
Abstract
xact penalty methods form an important class of methods for solving constrained optimization problems. Using penalty functions, the original constrained optimization problem can be transformed in an “equivalent” unconstrained problem. In this chapter we show how grossone can be utilized in constructing exact differentiable penalty functions for the case of only equality constraints, the general case of equality and inequality constraints, and quadratic problems. These new penalty functions allow to recover the solution of the unconstrained problem from the finite term (in its grossone expansion) of the optimal solution of the unconstrained problem. Moreover, Lagrangian duals associated to the constraints are also automatically obtained from the infinitesimal terms. Finally a new algorithmic scheme is presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
