A universal algorithm for linear and quadratic programming in the problems of contact deformation of cable-stayed structures with one-way connections

Abstract

Problems in production activities that require optimization problems are extremely numerous and very diverse. Optimization approaches are most often associated with the search for the best version of a structure or building. Mathematical methods for solving such problems are developing rapidly and are widely used. They actively and productively penetrate into many areas of scientific research, into engineering and design developments, are an important tool for improving design efficiency throughout the entire process of creating structures. The search for the best design solution is reduced to the selection of a set of parameters that provide a stationary value of the objective function. A wide range of extreme problems of practical orientation, as a rule, in mathematical models contains restrictions on design parameters of the equality-inequality type. In general, their set makes up the content of such a section of mathematics as Mathematical Programming. Due to the fact that there is no single solution method, diversity in research approaches has formed, which divides them into groups, classes, etc. Linear programming (LP), as one of the sections, with a linear objective function and constraints is well studied and successfully applied. Methods of solving problems of nonlinear programming, which includes quadratic programming, are more complex. Therefore, the development of convenient computational schemes is relevant. The essence of this work is that the statements of 2 optimization problems are formalized in a single and convenient form of a symmetric matrix dependence, which makes it possible to obtain an effective (in our opinion) algorithm for their implementation. Namely, a unified scheme for solving both LP and KP problems based on matrix algebra operations is proposed. Quadratic programming (QP), as the second section, also has wide possibilities, in particular, it allows considering the practical tasks of calculating VAT in the mechanics of a deformed solid body under the conditions of contact interaction. Such problems, in particular, include cable-stayed structures with one-way connections and span lengths that can reach tens or hundreds of meters. As an example, the behavior of a model cable-stayed span structure under varying wind loads is considered. The given results may be of interest.