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Abstract This paper presents an optimal control problem to analyze the efficacy of counter-terrorism tactics. We present an algorithm that efficiently combines the Minimum Principle of Pontryagin, the shooting method and the cyclic descent of coordinates. We also present a result that allows us to know a priori the steady state solutions. Using this technique we are able to choose parameters that reach a specific solution, of which there are two. Numerical examples are presented to illustrate the possibilities of the method. Finally, we study the sufficient conditions for optimality and suggest an improvement on the functional which also guarantees local optimality. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the profit-maximization problem, considering maximum constraints for the general case of m-inputs and using the Cobb–Douglas model for the production function. To do so, we previously study the firm’s cost minimization problem, proposing an equivalent infimal convolution problem for exponential-type functions. This study provides an analytical expression of the production cost function, which is found to be a piece-wise potential. Moreover, we prove that this solution belongs to class C 1. Using this cost function, we obtain the explicit expression of maximum profit. Finally, we illustrate the results obtained in this paper with an example. [Copyright &y& Elsevier]

Abstract: This paper addresses a hydrothermal problem that simultaneously considers non-regular Lagrangian and non-holonomic inequality constraints, obtaining a necessary minimum condition. It is further shown that the discontinuity of the lagrangian does not translate as discontinuity in the derivative of the solution. Finally, a solution algorithm is developed and applied to an example. [Copyright &y& Elsevier]

Abstract: This paper studies the optimization of large-scale hydrothermal power systems. For the general problem with n hydro-plants, we present an algorithm using a particular strategy related to the Gauss–Southwell method of nonlinear optimization. The algorithm offers a constructive method for producing sequences of problems with one hydro-plant. For this simple problem we use Pontryagin’s minimum principle to prove a condition for the extremals of the functional. We set out our problem in terms of optimal control in continuous time, with the Bolza-type functional. Finally, we present one example employing a program developed with the “Mathematica” package and analyze the convergence of the algorithm. [Copyright &y& Elsevier]