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In this paper a general formulation for the kinetics of multi-step enzymatic reactions is presented. The optimal enzyme and metabolite concentrations are studied for the problem of minimizing the operation time in which the substrate is converted into the product. We give an analytic solution for three different kinetic models for both the unbranched and branched cases. Sufficient conditions for the optimality of the solution are studied. Several examples are presented. [ABSTRACT FROM AUTHOR]

The infimal convolution operation arises in mathematical economics in the analysis of several problems. In this paper we first present a survey and summarize two previous papers by the authors on the classic firm's cost-minimization problem. Moreover, we present a new application: the analytical solution of the utility maximization problem which we shall obtain applying the supremal convolution operation. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of optimal control problems inspired by the hydroelectric context. These problems model a continuous production process with several interrelated pre-set availability inputs in a finite time interval with production functions which are linear with respect to the consumption rate over time. It constitutes a bang–singular–bang control problem, which we solve using a cyclic coordinate descent strategy combined with a suitable adaptation of the shooting method. Finally, the proposed algorithm is implemented using the Mathematica package and applied to a hydraulic optimization problem in which the potential of the algorithm is evidenced. [ABSTRACT FROM AUTHOR]

This paper presents a method to solve the economic dispatch (ED) problem for thermal unit systems involving combined cycle (CC) units. The ED problem finds the optimal generation of each unit in order to minimize the total generation cost while satisfying the total demand and generating-capacity constraints. A CC unit presents multiple configurations or states, each state having its own unique cost curve. Therefore, in performing ED, we need to be able to shift between these cost curves. Moreover, the cost curve is not convex for some of these states. Hence, ED becomes a non-convex optimization problem, which is difficult to solve by conventional methods. In this paper we present a new technique, developed to find the global solution, that is based on the calculation of the infimal convolution. The paper includes the results for a case test and we compare our solution with other techniques. [ABSTRACT FROM PUBLISHER]

In this paper we present a generalization of the classic Firm's profit maximization problem, using the linear model for the production function, considering a non constant price and maximum constraints for the inputs. We formulate the problem by previously calculating the analytical minimum cost function. This minimum cost function will be calculated for each production level via the infimal convolution of quadratic functions and the result will be a piecewise quadratic function. To solve this family of optimization problems, we present an algorithm of quasi-linear complexity. Moreover, the resulting cost function in certain cases is not $$C^{1}$$ and the profit maximization problem will be solved within the framework of nonsmooth analysis. Finally, we present a numerical example. [ABSTRACT FROM AUTHOR]

Abstract: The problem of economic dispatch with multiple fuel units has been widely addressed via different techniques using approximate methods due to the exponential complexity of full enumeration in the underlying combinatory problem. A method has recently been outlined by Min et al. (2008), that allows the problem to be solved in an exact way in polynomial time. In this paper, we present an alternative technique and take this idea further, studying and comparing two algorithms of polynomial complexity: basic recurrence and divide-and-conquer. Moreover, we provide the exact solution to the problem by Lin and Viviani (1984), that constitutes the traditional test for all approximate methods and present a comprehensive survey of several heuristic approaches. [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]