Multiplier Method for Nonlinear Programming

Trajectory Optimization for a Multistage Launch Vehicle Using Nonlinear Programming

This work is an example of application of nonlinear programming to a problem of three-dimensional trajectory optimization for multistage launch vehicles for geostationary orbit missions. The main objective is to minimize fuel consumption or equivalently to maximize the payload. The launch vehicle considered here, Europa-II, consists of 5 thrust phases and 2 coast phases. Major parameters of the...

Multiplier Methods for Nonlinear Optimal Control

Error estimates are derived for an augmented Lagrangian approximation to an optimal control problem. Convex control constraints are treated explicitly while a Lagrange multiplier is introduced for the nonlinear system dynamics. The nonlinear optimal control problem does not fit the classical theory for estimating the error in multiplier approximations, since the natural coercivity assumption is...

A dynamic programming approach for solving nonlinear knapsack problems

Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...

Modified Gauss Elimination Technique for Separable Nonlinear Programming Problem

A nonlinear interval number programming method for uncertain optimization problems

In this paper, a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints. Based on an order relation of interval number, the uncertain objective function is transformed into two deterministic objective functions, in which the robustness of design is considered. Through a modified po...