An approach to nonlinear constrained mathematical programming problems which makes use of a second order derivative is presented. By using a second order modified objective function method, a modified optimization problem associated with a primal mathematical programming problem is constructed. This auxiliary optimization problem involves a second order approximation of an objective function co...

An appealing feature of interior methods for linear programming is that the number of iterations required to solve a problem tends to be relatively insensitive to the choice of initial point. This feature has the drawback that it is difficult to design interior methods that efficiently utilize information from an optimal solution to a “nearby” problem. We discuss this feature in the context of ...

The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods ...

A new and simple method based on constrained nonlinear programming concepts is being proposed in this research to interpret the self-potential (SP) anomaly due to two-dimensional inclined sheets of finite depth extent. A constrained nonlinear model has been formulated to describe the geophysical problem related to this buried inclined structure. Thereafter this model has been solved by the famo...

In this paper, a Model Predictive Control problem for constrained nonlinear systems with quantized input is formulated and represented as a multiparametric Nonlinear Integer Programming (mp-NIP) problem. Then, a computational method for explicit approximate solution of the resulting mp-NIP problem is suggested. The proposed approximate mp-NIP approach is applied to the design of an explicit app...

Constrained nonlinear programming problems often arise in many engineering applications. The most well-known optimization methods for solving these problems are sequential quadratic programming methods and generalized reduced gradient methods. This study compares the performance of these methods with the genetic algorithms which gained popularity in recent years due to advantages in speed and r...

I. A Brief History of Optimization Research: The history of optimization of realvalued non-linear functions (including linear ones), unconstrained or constrained, goes back to Gottfried Leibniz, Isaac Newton, Leonhard Euler and Joseph Lagrange. However, those mathematicians often assumed differentiability of the optimand as well as constraint functions. Moreover, they often dealt with the equal...