An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular cases, the minimum in the problem is known to be equal to the tropical spectral radius of the matrix. We examine the problem in the common setting of a general ...

Out-of-sample embedding techniques insert additional points into previously constructed configurations. An out-of-sample extension of classical multidimensional scaling is presented. The out-of-sample extension is formulated as an unconstrained nonlinear least-squares problem. The objective function is a fourth-order polynomial, easily minimized by standard gradient-based methods for numerical ...

One of the possible ways of solving general problems of constrained nonlinear optimization is to convert them into a sequence of unconstrained problems. Then the need arises to solve an unconstrained optimization problem reliably and efficiently. For this aim, Newton methods are usually applied, often in combination with sparse Cholesky decomposition. In practice, however, this approach may not...