On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.

On Certain Problems of Identification of Thermal Density of the Temperature State of the Hollow Cylinder Shell

Introduction. In conditions of the active use of composite materials, as when accomplishing the tasks of extending the service life of existing structures, problems on recovering unknown parameters of their components under the known data on their surface arise. In [1-4], to solve the problems of identification ofparameters of a wide range, it is proposed to construct explicit expressions of the gradients of residual functionals by means of the corresponding conjugate problems obtained from the theory of optimal control of the states of multicomponent distributed systems, which is the development of the corresponding researches of Zh. Lyons. In [5-7], this technology is extended to the problem of thermoelastic deformation of multicomponent bodies. In this article some problems of optimal control of the temperature state of a cylindrical body with a cavity are considered. The purpose of the paper is to show the algorithm for identifying the parameters of a cylindrical hollow shell, based on the theory of optimal control and using the gradient methods of Alifanov. Results. Based on the theory of optimal control, the temperature control of a cylindrical shell is studied. To solve the problem of identifying the parameters of a hollow cylindrical shell, namely, finding the heat flux powers on its surfaces, based on [1,2,5-7], a direct and conjugate problem and gradients of non-viscous functionals are constructed. Discretization by the finite element method using piecewise quadratic functions is carried out and accuracy estimates for it are presented. The initial problem in the model examples presented is solved using gradient methods, where at each step of determining the (n + 1) the approximation of the solution, the direct and adjoint problems are solved using finite element method with the help piecewise quadratic functions by minimizing the corresponding energy functional. A number of model examples solved.

Solving the problem of combination of Multi-fuel electric generator units using lagrange multiplier theory

This paper presents an approach to solve the unit commitment problem with multifuel options in the thermal power plants. Traditionally, each generator unit is used to each fuel option with the segmented piecewise quadratic functions, so that it is not difficult to solve them. However, it is more realistic to represent the fuel cost function for each fossil fired plant as the segmented piecewise quadratic functions. Those units are faced with the difficulty of determining which fuel is the most economical to burn. Therefore, this paper presents an approach to solve the unit commitment problem with multi-fuel options. An advantage of the method is to formulate Lagrange mathematical function easily based on the Lagrange multiplier theory. The simulation result for 10 generator systems are compared with others methods to show that the approach is a new method and an effective method to solve the minimizing of electricity production cost of generator units with multi-fuel option.

TOPOLOGY-GUIDED TESSELLATION OF QUADRATIC ElEMENTS

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to the piecewise-quadratic function. In particular, the tessellation is used for computing the Reeb graph, a topological data structure that provides a succinct representation of level sets of the function.