Ibragimov, D. N. Novozhilin, N. M. Portseva, E. Yu.
Published in
Automation and Remote Control

Abstract We consider the solution of the speed problem for linear time-varying discrete-time systems with convex control constraints. A method is proposed for reducing the general case of the speed problem to the case of linear control constraints using polyhedral approximation algorithms. Sufficient optimality conditions for the guaranteed solutio...

Chelishchev, Petr Sørby, Knut
Published in
International Journal of Metrology and Quality Engineering

This paper presents algorithms for estimating the minimum volume bounding box based on a three-dimensional point set measured by a coordinate measuring machine. A new algorithm, which calculates the minimum volume with high accuracy and reduced number of computations, is developed. The algorithm is based on the convex hull operation and established...

Kuvshinov, D. R. Osipov, S. I.
Published in
Automation and Remote Control

We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum po...

Lijingjiao, Iila

In a quest to design novel deployable structures, flexible polyhedra provide interesting insights. This work follows the discovery of flexible polyhedra and aims to make flexible polyhedra more useful. The dissertation describes how flexible polyhedra can be made. The flexible polyhedra first considered in this dissertation have a rotational degree...

Gabidullina, Z. R.
Published in
Lobachevskii Journal of Mathematics

This paper is aimed at presenting a systematic exposition of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). We have concentrated on the convex polyhedron given as a convex hull of finitely many vectors of the space. We investigated the reduction of the p...

Contesse, Luis Hiriart-Urruty, Jean-Baptiste Penot, Jean-Paul

With the help of elementary results and techniques from Real Analysis and Optimization at the undergraduate level, we study least squares solutions of linear inequality systems. We prove existence of solutions in various ways, provide a characterization of solutions in terms of nonlinear systems, and illustrate the applicability of results as a mat...

Voytekhovsky, Yu. L.
Published in
Journal of Structural Chemistry

E. S. Fedorov’s algorithm allowing us to obtain the full combinatorial diversity of convex polyhedra from the tetrahedron is considered in the paper. The latest results on the number of combinatorially different convex n-hedra for the given n and their point symmetry groups are presented. Possible applications of the results are shown. The problems...

Bakhanovich, S. V. Sobolevskii, P. I.
Published in
Computational Mathematics and Mathematical Physics

Aspects of parametrized tiling as applied to algorithms whose computational domain can be represented as a convex polyhedron are studied. A method for constructing approximations to a set of tiles is developed, and necessary and sufficient conditions for their accuracy are stated. Formulas for determining intertile vectors are derived. A formal rep...

German, V. N.
Published in
Cybernetics and Systems Analysis

Practical methods are proposed to solve linear constraints over real and rational fields with quantifiers. Secondary problems are observed together with the set of possible solutions in the context of automatic software model verification.

Zalgaller, V. A.
Published in
Siberian Mathematical Journal

We select a class of pyramids of a particular shape and propose a conjecture that precisely these pyramids are of greatest surface area among the closed convex polyhedra having evenly many vertices and the unit geodesic diameter. We describe the geometry of these pyramids. The confirmation of our conjecture will solve the “doubly covered disk” prob...