We examine two multidimensional optimization problems that are formulated in terms of tropical mathematics. The problems are to minimize nonlinear objective functions, which are defined through the multiplicative conjugate vector transposition on vectors of a finite-dimensional semimodule over an idempotent semifield, and subject to boundary constraints. The solution approach is implemented, which involves the derivation of the sharp bounds on the objective functions, followed by determination of vectors that yield the bound. Based on the approach, direct solutions to the problems are obtained in a compact vector form. To illustrate, we apply the results to solving constrained Chebyshev approximation and location problems, and give numerical examples.
|Title of host publication||Mathematical Methods and Optimization Techniques in Engineering: Proc. 1st Intern. Conf. on Optimization Techniques in Engineering (OTENG '13), Antalya, Turkey, October 8-10, 2013|
|Publisher||WSEAS - World Scientific and Engineering Academy and Society|
|Pages||242 стр., 86-91|
|Publication status||Published - 2013|
Krivulin, N., & Karel, Z. (2013). Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints. In Mathematical Methods and Optimization Techniques in Engineering: Proc. 1st Intern. Conf. on Optimization Techniques in Engineering (OTENG '13), Antalya, Turkey, October 8-10, 2013 (pp. 242 стр., 86-91). WSEAS - World Scientific and Engineering Academy and Society.