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The MATLAB/DIDO toolbox does not require a "guess" to run the algorithm. This and other distinguishing features have made DIDO a popular tool to solve optimal control problems. [4] [7] [15] The MATLAB optimal control toolbox has been used to solve problems in aerospace, [11] robotics [1] and search theory. [2]
In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem.It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem.
Linear programming problems are optimization problems in which the objective function and the constraints are all linear. In the primal problem, the objective function is a linear combination of n variables. There are m constraints, each of which places an upper bound on a linear combination of the n variables. The goal is to maximize the value ...
In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine solving the second problem exists, then the first problem can be solved by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times.
Cournot's model of competition is typically presented for the case of a duopoly market structure; the following example provides a straightforward analysis of the Cournot model for the case of Duopoly. Therefore, suppose we have a market consisting of only two firms which we will call firm 1 and firm 2.
A duopoly (from Greek δύο, duo ' two '; and πωλεῖν, polein ' to sell ') is a type of oligopoly where two firms have dominant or exclusive control over a market, and most (if not all) of the competition within that market occurs directly between them. Duopoly is the most commonly studied form of oligopoly due to its simplicity.
Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb, [ 4 ] Binh et al. [ 5 ] and Binh. [ 6 ] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which ...
GPOPS-II [3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where is the number of phases): = ((), …, ()) subject to the dynamic constraints