ALGORITHM FOR SOLVING THE PROBLEM OF QUADRATIC PROGRAMMING WITH CONSTRAINTS, CONTAINING THE PARAMETER
This work is devoted to the construction of an algorithm for solving the problem of quadratic programming with restrictions of the type of equations and inequalities, one of which (restriction-equality) contains a parameter. Mathematically, the solution of this problem is based on the modified Lagrange multiplier method, which allows parametrically determining the sought variables as functions of the entered parameterl. Graphics of sought functions represent piecewise polyline. Those parameter l values, in which at least one of the functions suffers a fracture, will be angular, and their corresponding vectors, consisting of values of the sought functions, will be angular vectors. Angular vectors deliver a conditional extremum to the initial problem. The vector, which is a linear combination of two adjacent angular vectors, will also deliver a conditional extremum to the original problem. On the basis of the proposed computational algorithm in the form of a flowchart, a graphical solution of the problem is constructed, which can also be written in tabular form. The article provides a test example, describing the application of this algorithm in solving the applied problem of financial asset management, namely, determining the effective set of optimal portfolios in general, when the function of risk assessment associated with investing in a portfolio is minimized, and the expected return of the portfolio is equal to an arbitrary value m from a certain interval.