title: ÐÐ¾Ð´Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ñ Ð¸Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸ÐµÐ¹ Ð² ÐÐ "ÐÐÐ¢Ð£"
title: Ð¼Ð°Ð³Ð¸ÑÑÐµÑÑÐºÐ°Ñ Ð´Ð¸ÑÑÐµÑÑÐ°ÑÐ¸Ñ
titleType: Subtitle
Creators: name: ÐÐ»ÐµÐ¿Ð°Ñ, ÐÐ°ÑÐ¸Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2016
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÐÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ
ÐÑÐ¿ÑÐºÐ»Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
mathematical programming
nonlinear programming
convex programming
Lagrange's equations

description: ÐÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ñ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ Ð½Ð¾Ð²ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ, Ð¾ÑÐ½Ð¾ÑÑÑÐ¸ÑÑÑ Ðº ÐºÐ»Ð°ÑÑÑ Ð·Ð°Ð´Ð°Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐµÐ»ÐµÐ²Ð¾Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¸ Ð½Ð° Ð²ÑÐ¿ÑÐºÐ»ÑÑ Ð¸ Ð½ÐµÐ²ÑÐ¿ÑÐºÐ»ÑÑ Ð¾Ð±Ð»Ð°ÑÑÑÑ Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹. Ð Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð»ÐµÐ¶Ð°Ñ ÑÐ¿Ð¾ÑÐ¾Ð±Ñ ÑÐ²ÐµÐ´ÐµÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼Ñ Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ² ÐºÐ°Ðº Ðº Ð¾Ð´Ð½Ð¾Ð¼Ñ ÑÐ°Ð²Ð½Ð¾ÑÐ¸Ð»ÑÐ½Ð¾Ð¼Ñ Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ²Ñ, ÑÐ°Ðº Ðº Ð¾Ð´Ð½Ð¾Ð¼Ñ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð¼Ñ ÑÐ¾Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ñ (ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ), Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐµÐ¼Ñ Ð»Ð¸Ð±Ð¾ Ð¾Ð±Ð»Ð°ÑÑÑ Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹, Ð»Ð¸Ð±Ð¾ Ð³ÑÐ°Ð½Ð¸ÑÑ ÑÑÐ¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸. ÐÐ¾ÑÐ»ÐµÐ´Ð½ÐµÐµ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ð»Ð¾ ÑÐ¾ÑÐ¼Ð°Ð»ÑÐ½Ð¾ ÑÐ²ÐµÑÑÐ¸ Ð¸ÑÑÐ¾Ð´Ð½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ðº ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼ Ð·Ð°Ð´Ð°ÑÐ°Ð¼ ÐÐ°Ð³ÑÐ°Ð½Ð¶Ð° Ð¸ Ð¾ÑÑÑÐµÑÑÐ²Ð»ÑÑÑ Ð¸Ñ ÑÐµÑÐµÐ½Ð¸Ðµ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐ¼Ð¸ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼Ð¸, Ð² ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸, Ð¼ÐµÑÐ¾Ð´Ð°Ð¼Ð¸ Ð½ÐµÐ¿ÑÐµÑÑÐ²Ð½Ð¾Ð³Ð¾ Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ° (Ð½Ð°Ð¸Ð±ÑÑÑÑÐµÐ¹ÑÐµÐ³Ð¾ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ° Ð¸Ð»Ð¸ Ð¿Ð¾Ð´ÑÐµÐ¼Ð°), Ð¾Ð±ÐµÑÐ¿ÐµÑÐ¸Ð²Ð°ÑÑÐ¸Ð¼Ð¸ Ð¾ÑÑÑÐºÐ°Ð½Ð¸Ðµ Ð»Ð¾ÐºÐ°Ð»ÑÐ½ÑÑ Ð¾Ð¿ÑÐ¸Ð¼ÑÐ¼Ð¾Ð². ÐÐ»Ñ Ð¾ÑÑÑÐºÐ°Ð½Ð¸Ñ ÑÐºÑÑÑÐµÐ¼ÑÐ¼Ð° Ð¿ÑÐ¸ ÐµÐ³Ð¾ Ð½Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ð¸ Ð½Ð° Ð³ÑÐ°Ð½Ð¸ÑÐµ Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð¸ Ð½ÐµÐ²ÑÐ¿ÑÐºÐ»Ð¾Ð¹, Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÐ¹ Ð½Ð° Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸Ð´ÐµÐ¹ Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÐ¾ÑÐ¸Ð¸ Ð³Ð¾Ð»Ð¾Ð½Ð¾Ð¼Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼ Ð¸ ÑÐµÐ³ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»ÑÐ½ÑÑ ÑÐ¾Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ð¹. Ð ÐµÑÐµÐ½Ð° Ð²Ð°Ð¶Ð½Ð°Ñ Ð¿ÑÐ¸ÐºÐ»Ð°Ð´Ð½Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ° Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ ÑÐ¾Ð´Ð° Ð¸ ÑÐ³Ð»Ð° Ð¿ÐµÑÐµÐºÐ»Ð°Ð´ÐºÐ¸ ÑÑÐ»Ñ Ð´Ð»Ñ Ð¼Ð¸Ð½Ð¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð¿ÐµÑÐµÑÐ¾Ð´Ð° ÐºÐ¾ÑÐ°Ð±Ð»Ñ Ð½Ð° Ð½Ð¾Ð²ÑÐ¹ ÐºÑÑÑ Ð¿ÑÐ¸ Ð¾Ð³ÑÐ°Ð½Ð¸ÑÐµÐ½Ð¸ÑÑ, Ð½Ð°Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÑ Ð½Ð° ÑÐ³Ð¾Ð» ÐºÑÐµÐ½Ð°, ÑÑÐ¾ Ð¿ÑÐ¸Ð²Ð¾Ð´Ð¸Ñ Ðº Ð½ÐµÐ²ÑÐ¿ÑÐºÐ»Ð¾Ð¹ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹.
description: Proposed and investigated new methods of solving mathematical programming problems belonging to the class of optimization problems the objective function on convex and non-convex regions of admissible solutions. In the basis of the proposed methods lie in the ways information systems of inequalities as one inequality is equivalent to, the functional relationship (equation) describing the area of valid solutions, or the boundary of this region. The latter allowed formally to reduce the original problem to the classical tasks of Lagrange and implement their solution by different methods, in particular methods continuous gradient (differential rapid descent or ascent), providing finding local Optima. To find extremum at its location on the border of the admissible region that may be nonconvex, the proposed algorithm based on the use of ideas and methods of the theory of holonomic systems and regulation of functional relations. Solved an important applied problem of the optimization of speed and rudder angle to minimize the transit time of the ship on a new course under the constraints imposed on the roll angle, which leads to a nonlinear non-convex region of feasible solutions.