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The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties....
In this paper, the augmented Lagrangian method is investigated for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The objective function of stochastic linear programming problem is piecewise linear and non-differentiable. Therefore, to use a smooth optimization methods, the objective function is approximated by a differentiable and piecewise quadratic function. Using quadratic approximation, it is required to obtain the...
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