Summary In this work, we propose a new algorithm for solving linear programs. This algorithm starts by an initial support feasible solution, then it moves from one feasible point to a better one following a new hybrid direction. The constructed direction gives a better local improvement of the objective function than the direction of the adaptive method with hybrid direction (AMHD) algorithm proposed in Bibi MO, Bentobache M. A hybrid direction algorithm for solving linear programs. International Journal of Computer Mathematics, 2015; 92(2):200‐216. In order to stop the algorithm, a suboptimality criterion is used and the long step rule is developed for changing the current support. The proposed algorithm is implemented with C++, then a numerical study is conducted on randomly generated test problems and some instances of an optimal control problem. The obtained numerical results show that our algorithm is competitive with AMHD and the primal simplex algorithm of GNU linear programming kit (GLPK).

In this work, we calculated the optimal heel angle trajectory of a rocket which have a constant mass and moves with a nonrectilinear motion from an initial point to a final one with a known altitude. The objective of the study is to maximize the lateral offset of the rocket. This problem is modelled as a nonlinear optimal control problem, where the control represents the heel angle of the rocket. In order to solve numerically the problem, we applied the shooting method which is based on the Pontryagin's maximum principle, then we developed an implementation with the MATLAB programming language. Finally, we presented simulation results which show the fast convergence and the accuracy of the shooting method.

This paper proposes a new technique for the optimization of multi-frequency tests for linear analog circuits. Fault simulation is used to obtain the frequency intervals for the detection of each fault. New efficient algorithms are then presented for the selection of the optimal set of test frequencies within these intervals for the detection of all faults. Numerical simulations with randomly generated problem instances demonstrate the good time complexity of the proposed algorithms, with a large improvement over previous approaches (Mir et al 1996).

In this paper we show that the problem of minimizing the number of test frequencies necessary to detect all possible faults in a multi-frequency test approach for linear analog circuits can be modeled as a set covering problem. We will show in particular, that under some conditions on the considered faults, the coefficient matrix of the problem has the strong consecutive-ones property and hence the corresponding set covering problem can be solved in polynomial time. For an efficient solution of the problem, an interval graph formulation is also used and a polynomial algorithm using the interval graph structure is suggested. The optimization of test frequencies for a case-study biquadratic filter is presented for illustration purposes. Numerical simulations with a set of randomly generated problem instances demonstrate two different implementation approaches to solve the optimization problem very fast, with a good time complexity.