Abstract:

The objective of this paper is to propose an exact l1 penalty method for
constrained interval-valued programming problems which transform the constrained
problem into an unconstrained interval-valued penalized optimization problem. Under
some suitable conditions, we establish the equivalence between an optimal solution of
interval-valued primal and penalized optimization problem. Moreover, saddle-point
type optimality conditions are also established in order to find the relation between an
optimal solution of penalized optimization problem and saddle-point of Lagrangian
function. Numerical examples are given to illustrate the derived results.

Key words: Exact l1 penalty method ·, Interval-valued programming ·, Convexity ·, LU
optimal ·, Optimality conditions ·, Saddle-points