Informatica

This paper reviews the interplay between global optimization and probability models, concentrating on a class of deterministic optimization algorithms that are motivated by probability models for the objective function. Some complexity results are described for the univariate and multivariate cases.

In this paper, we consider the so-called structured low rank approximation (SLRA) problem as a problem of optimization on the set of either matrices or vectors. Briefly, SLRA is defined as follows. Given an initial matrix with a certain structure (for example, Hankel), the aim is to find a matrix of specified lower rank that approximates this initial matrix, whilst maintaining the initial structure. We demonstrate that the optimization problem arising is typically very difficult; in particular, the objective function is multiextremal even in simple cases. We also look at different methods of solving the SLRA problem. We show that some traditional methods do not even converge to a locally optimal matrix.

We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a random objective function distributed according to the Wiener measure.

One of the most known applications of Discrete Optimization is on scheduling. In contrast, one of the most known applications of Continuous Nonlinear Optimization is on the control of dynamic systems. In this paper, we combine both views, solving scheduling problems as dynamic systems, modeled as discrete-time nonlinear optimal control problems with state and control continuous variables subjected to upper and lower bounds. Complementarity constraints are used to represent scheduling decisions. One example we discuss in detail is the crude oil scheduling in ports, with numerical results presented.

We consider finite population slotted ALOHA where each of n terminals has its own transmission probability pi. Given the overall traffic load λ, the probabilities pi are determined in such a way as to maximize throughput. This is achieved by solving a constrained optimization problem. The results of Abramson (1970) are obtained as a special case. Our recent results are improved (Mathar and Žilinskas, 1993).