We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with addition and invertible multiplication). The are to minimize objective functions given by analogues of multivariate Puiseux polynomials, subject box constraints variables. A technique for variable elimination is pre...

In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the num...

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed component f , and a variable component b that is proportional to the field-of-view area. When only one type of sensor or, in general, one type of disc, is availa...

In the Line Cover problem a set of n points is given and the task is to cover the points using either the minimum number of lines or at most k lines. In Curve Cover, a generalization of Line Cover, the task is to cover the points using curves with d degrees of freedom. Another generalization is the Hyperplane Cover problem where points in d-dimensional space are to be covered by hyperplanes. Al...