Sharif Digital Repository

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... 

This research studied optimal combination therapy of diseases with uncertain evolutionary dynamics. The problem of neutralizing HIV virus in the host’s body was modeled as a convex optimization problem whose objective function is minimizing disturbance effect while the disease dynamics is stable in the presence of polytopic uncertainty.In the first part of this thesis, according to the characteristics of positive systems, the convexity of H2 and H∞ in the presence of polytopic uncertainty was shown. To solve the minimization problem of disturbance effect, an algorithm based on minimizing a cutting plane was used. This algorithm, with solving the minimization problem iteratively in each step... 

Magnetic Resonance Imaging (MRI) is a non-invasive imaging modality which can represents the structure, metabolism and the function of inner tissues and organs. Unlike other imaging modalities MRI does not use ionizing radiation.Reducing the imaging time will result in cost reduction and patient comfort. Therefore since the invention of MRI, increasing the speed of imaging has drawn a lot of attention. This was mainly done by improving and upgrading the data collecting hardware of the imaging module.With the advances in technology, a point has been nearly reached, that due to the physical and physiological constraints, such as nerve stimulation, quickening the hardware is impractical.... 

In this thesis, the optimal control structure selection and design of sparse multi-variable control systems is addressed. A fundamental challenge which frequently emerges in engineering, social, and economic sciences, is the optimal selection of a subset of elements, in order to maximally fulfil a design objective. In practice, it is required to solve this underlying selection problem in conjunction with a non-linear or non-convex optimization which is designed to ensure desired performance. The requirement to solve these two problems simultaneously is what makes it inherently difficult; one which has thus far eluded efforts to develop a systematic means of determining its solution. In spite... 

Due to the prominence of low-order controllers in industry, this thesis intends to improve the common design algorithms in this field. In this regard, the main challenge is that this problem is NP-hard due to the non-convex rank constraint which appears in the formulation. The existing algorithms mostly solve this problem by obtaining a convex sub-space for this constraint and using output feedback convex optimization methods.Two of common algorithms are non-iterative. These methods two main steps; first to obtain the full-order Lyapunov matrices related to the controller, and then, to fix the null-space of the matrices which have rank constraint. One of the advantages of the algorithm... 

In this thesis, various methods for solving the classification problem with algorithms for some of their estimations, will be discussed. First, linear discriminant analysis (LDA), which is the most basic likelihood based method of classification is studied. In the next section, regularized discriminant analysis, a version of LDA in which the covariance matrix of each class is shrank toward the identity matrix, is studied. Then the ridge fusion in which a penalty is added to the likelihood function so that in the joint estimation of covariance matrices of dierent classes, all arrays become equal as much as possible is discussed. In the joint graphical lasso,precision matrices of dierent... 

The problem of learning using high volume of data as stream, has attracted much attention recently. In this thesis, the problem is modeled and analized using Online Convex Optimization tools [1], [2]. General performance bounds are stated and clarified in this framework [8]. Using the practical experience in Online Decision Making (e.g., predicting price in Stock Market), the need for a more flexible model, which adapts to changes in problem, is presented. In this thesis, after reviewing the literature and online convex optimization framework, we will define ”Concept Drift”, which describes changes in the dynamics of the problem and the statistical tools to detect it [13], [5]. And finally,... 

Waveform design for Target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works considered signal independent noise and found optimal signals for an estimation algorithm, here we extend the results to the case where clutter is also present and then we will find the optimum waveform for several estimators differing in the assumptions on the given statistics. Several different approaches to the optimal waveform design are proposed, including minimizing the error of MMSE estimator, minimizing the maximum error of the covariance shaping least square (CSLS) estimator and minimizing the MSE error of scaled least square (SLS)... 

One of the most important problems in online learning is a prediction with expert advice. In each step we make our prediction not only based on previous observation but also use expert information. In this thesis, we study the different well-known algorithms of expert advice and generalize problems when data arrival is in the two-dimensional grid. regret is a well-studied concept to evaluate online learning algorithm. online algorithm when data arrive consecutively in T time step has regret O (√(T)) . regret in two-dimensional grid with T row and P column is O(T√(P)).
2010 MSC: 68Q32 ; 68T05 ; 90C27  

This thesis addresses the problem of optimal distributed control of unknown interconnected systems. In order to deal with this problem, a data-driven learning framework for finding the optimal centralized and the suboptimal distributed controllers has been developed via convex optimization.First of all, the linear quadratic regulation (LQR) problem is formulated into a nonconvex optimization problem. Using Lagrangian duality theories, a semidefinite program is then developed that requires information about the system dynamics. It is shown that the optimal solution to this problem is independent of the initial conditions and represents the Q-function, an important concept in reinforcement... 

In the behavior of many convex optimization problems with random constraints in high dimensions, sudden changes or phase transitions have been observed in terms of the number of constraints. A well-known example of this is the problem of reconstructing a thin vector or a low-order matrix based on a number of random linear observations. In both cases, methods based on convex optimization have been developed, observed, and proved that when the number of observations from a certain threshold becomes more (less), the answer to the problem with a probability of close to one (zero) is correct and the original matrix is reconstructed. Recently, results have been obtained that explain why this...