In this work, we propose an algorithm for finding an approximate global minimum of a concave quadratic function with a negative semi-definite matrix, subject to linear equality and inequality constraints, where the variables are bounded with finite or infinite bounds. The proposed algorithm starts with an initial extreme point, then it moves from the current extreme point to a new one with a better objective function value. The passage from one basic feasible solution to a new one is done by the construction of certain approximation sets and solving a sequence of linear programming problems. In order to compare our algorithm with the existing approaches, we have developed an implementation with MATLAB and conducted numerical experiments on numerous collections of test problems. The obtained numerical results show the accuracy and the efficiency of our approach.
In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.
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