Unconstrained Lagrangians in Nonlinear Programming

Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear Programming

In this paper we study general lp regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of the firstand second-order stationary points and hence also of local minimizers of the lp minimization problems. We extend some existing iterative reweighted l1 (IRL1) and l2 (IRL2) minimization methods to solve these problems and propose new variants fo...

Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-burmeister Ncp Functions

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functio...

Augmented Lagrangians in semi-infinite programming

We consider the class of semi-infinite programming problems which became in recent years a powerful tool for the mathematical modelling of many real-life problems. In this paper, we study an augmented Lagrangian approach to semi-infinite problems and present necessary and sufficient conditions for the existence of corresponding augmented Lagrange multipliers. Furthermore, we discuss two particu...

Hydrogen Distribution in Refinery with Nonlinear Programming

Unconstrained inverse quadratic programming problem

The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part of the quadratic form) provided that approximate estimates of the optimal solution of the direct problem and those of the target function to be minimized in...