Recently primal-dual interior-point methodology has proven to be an eeective tool in linear programming applications and is now being extended, with great enthusiasm to general nonlinear programming applications. The primary purpose of this current study is to develop and promote the belief that since Newton's method is a tool for square nonlinear systems of equations, the fundamental role of i...

This paper is concerned with chance constrained programming to deal with nonlinear optimization problems with random parameters. Specific Monte Carlo methods to evaluate the gradient and Hessian of probabilistic constraints are proposed and discussed. These methods are implemented in penalization optimization routines adapted to stochastic optimization. They are shown to reduce the computationa...

We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.

There are many cases that a nonlinear fractional programming, generated as a result of studying fractional stochastic programming, must be solved. Sometimes an approximate solution may be sufficient enough to start a new process of calculations. To this end, this author introduces a new linear approximation technique for solving a fractional chance constrained programming (CCP) problem. After i...

A new method is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of Sequential Quadratic Programming and Sequential Linearly-Constrained Programming, the new method approximately solves, at each iteration, an equality-constrained optimization problem. The bound constraints are handled in outer iterations by means of an Augmented Lag...

Abstract We study nonlinear optimization problems with a stochastic objective and deterministic equality inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural networks. propose an active-set sequential quadratic programming (StoSQP) algorithm that utilizes differentiable exact augmented Lagrangian as the merit fu...