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Active set and interior methods for nonlinear optimization.

Byrd, Richard H., Nocedal, Jorge (1998)

Documenta Mathematica

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A second order $η$ -approximation method for constrained optimization problems involving second order invex functions

Tadeusz Antczak (2009)

Applications of Mathematics

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A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order $η$ -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order $η$ -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between...

Reduction of dimensionality in dynamic programming-based solution methods for nonlinear integer programming.

Ram, Balasubramanian, Babu, A.J.G. (1988)

International Journal of Mathematics and Mathematical Sciences

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A duality theorem for complex nonlinear programming

C. Das, J. Parida (1977)

Matematički Vesnik

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Saddle points criteria via a second order $η$ -approximation approach for nonlinear mathematical programming involving second order invex functions

Tadeusz Antczak (2011)

Kybernetika

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In this paper, by using the second order $η$ -approximation method introduced by Antczak [3], new saddle point results are obtained for a nonlinear mathematical programming problem involving second order invex functions with respect to the same function $η$ . Moreover, a second order $η$ -saddle point and a second order $η$ -Lagrange function are defined for the so-called second order $η$ -approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution...

A comparative study on optimization methods for the constrained nonlinear programming problems.

Yeniay, Ozgur (2005)

Mathematical Problems in Engineering

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Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study

Sophie Jan (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original...

Second order convexity and a modified objective function method in mathematical programming

Tadeusz Antczak (2007)

Control and Cybernetics

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