Sharif Digital Repository

Worst-case complexity guarantees for non-convex optimization algorithms is a topic that have received increasing attention. Here , we review trust-region Newton methods recently proposed in the literature . After a slight modification of the main model , two methods are proposed : one of them is based on the exact solution of the sub-problem , and the other is based on the inexact solution of the sub-problem , such as ``trust-region Newton-conjugate gradient " method with the complexity bounds corresponding to the best known bounds for this class of algorithms . We implement the proposed algorithms and test the programs in the Python software environment  

In this thesis, arranged by [6], the multiplier method is used to solve the network problems with nonlinear constraints and the Newton-like methods are used for updating the required parameters. This method, recently proposed in the literature, is based on solving a sequence of nonlinear optimization subproblems, dependent on the main problem, such that sequence of solutions of these problems converge to the solution of the main problem. In fact, to obtain an acceptable approximation of the main solution, it is needed to solve just a finite number of nonlinear subproblems. The main idea of the multiplier methods is based on eliminating some constraints and adding a penalty term to the... 

Recently, the primal-dual interior point methods for nonlinear programming has attracted considerable attention. Here, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. This is a convex optimization problem which is equivalent to a nonlinear convex optimization problem having linear equality and inequality and quadratic inequality constraints. This problem is reduced to a convex optimization problem of lower dimension with only inequality constraints. Finally, the problem is solved... 

In this study, the modeling of shrink-fit connection was performed by considering the effect of friction on the connection. The behavior of a beam with shrink-fit connection was compared with the results of Adams software and the modeling accuracy was shown. Using both energy and Newton methods, the equations of motion of a rigid rotor consisting of two shafts connected by shrink-fit connection were obtained and the dynamic behavior of the rotor was investigated. Finally, the coupling parameters affecting the vibrations and stability of this rotor were introduced and the effect of each on the system behavior was shown.
 

Nowadays, solving large-scale unconstrained optimization problems has wide applications in data science and machine learning. Therefore, the development and analysis of efficient algorithms for solving unconstrained optimization problems is of great interest. Line search and trust region are two general frameworks for guaranteeing the convergence of algorithms for solving unconstrained optimization problems. Conjugate gradient (CG) methods and the conjugate residual (CR) balance by Hestenes and Stiefel, have been presented for solving linear systems with symmetric and positive definite coefficient matrices. The basic feature of CR, that is, residual minimization, is important and can be used... 

Motorcycle has one of the most complicated geometries and mechanisms and its kinematic, according to the articles surveyed, has always been expressed with approximation and simplification in the degrees of freedom and especially in the magnitude of the angles. Analyzing the dynamic model of bodies, using methods like Kane, Lagrange, Boltzmann-Hamel, Gibbs-Apple, Newton, Hamilton and Ross, lead to mechanism’s equations of motion. While the equations of motions, obtained from alternative methods, lead to the same result, but the number of differential equations and sometimes their order, are different in different methods, and therefore their numerical solving time for the body’s motion, are... 

Recently, Luc defined a dual program for a multiple objective linear program. The dual problem is also a multiple objective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established.Here, we use these results to establish some relationships between multiple objective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multiple objective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are...