In this paper, we consider the minimizing total weighted completion time in preemptive equal-length job with release dates scheduling problem on a single machine. This problem is known to be open. Here, we give some properties of optimal schedules for the problem and its special cases.
We study the characteristic features of the detection zone for an onboard radar station for an early radar detection system operating in the impulse–Doppler mode. We show that due to these features, there exist covert trajectories such that objects flying along such trajectories are not detected by this onboard radar station. We derive differential equations that define covert trajectories, find various forms of covert trajectories, and study their properties.
The theoretical fundamentals for solving the linear quadratic problems may be some times used to design the optimal control actions for the nonlinear systems. The method relying on the Riccati equation with state-dependent coefficients is promising and rapidly developing tools for design of the nonlinear controllers. The set of possible suboptimal solutions is generated by ambiguous representation of the nonlinear system as a linearly structured system with state-depended coefficients and the lack of sufficiently universal algorithms to solve the Riccati equation also having state-depended coefficients. The paper proposed a method to design a guaranteed control for the uncertain nonlinear plant with state-depended parameters. An example of design the controller for an uncertain nonlinear system was presented.
We propose an accelerated gradient-free method with a non-Euclidean proximal operator associated with the p-norm (1 ⩽ p ⩽ 2). We obtain estimates for the rate of convergence of the method under low noise arising in the calculation of the function value. We present the results of computational experiments.
We consider smooth convex optimization problems whose full gradient is not available for their numerical solution. In 2011, Yu.E. Nesterov proposed accelerated gradient-free methods for solving such problems. Since only unconditional optimization problems were considered, Euclidean prox-structures were used. However, if one knows in advance, say, that the solution to the problem is sparse, or rather that the distance from the starting point to the solution in 1-norm and in 2-norm are close, then it is more advantageous to choose a non- Euclidean prox-structure associated with the 1-norm rather than a prox-structure associated with the 1-norm. In this work we present a complete justification of this statement. We propose an accelerated descent method along a random direction with a non-Euclidean prox-structure for solving unconditional optimization problems (in further work, we propose to extend this approach to an accelerated gradient-free method). We obtain estimates of the rate of convergence for the method and show the difficulties of transferring the above-mentioned approach to conditional optimization problems.
The problem of building the rating of a remote training system by processing the results of a run of tests was considered. The Rasch model extended to a run of tests was used. A recurrent algorithm based on the maximum-likelihood procedure and the Newton method was proposed to calculate the rating.
A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. The ensembles of forecasting trajectories are generated by the sampling of the entropy-optimal probability distributions. This procedure is used for the randomized prediction of the daily electrical load of a regional power system. A stochastic oscillatory dynamic regression model is designed. One-, two-, and three-day forecasts of the electrical load are constructed, and their errors are analyzed.