Spelling suggestions: "subject:"semidefinite programming"" "subject:"semidefiniten programming""
1 
Cooperative Positioning in Wireless Sensor Networks Using Semidefinite ProgrammingMonir Vaghefi, Sayed Reza 06 February 2015 (has links)
With the rapid development of wireless technologies, the demand for positioning services has grown dramatically over the past three decades. The Global Positioning System (GPS) is widely used in wireless devices for positioning purposes. However, in addition to having bulky and expensive equipment, GPS receivers do not operate properly in dense and indoor environments. Difficulties in using GPS lead us to use sensor localization in which the position information is obtained from the measurements collected within the network without the aid of external resources. Sensor localization has been a great topic of interest during past decades. Although many positioning algorithms have been developed previously in the literature, positioning is still a challenging task. There are many factors that can affect the positioning performance if they are neglected or not treated properly. These factors introduce many nuisance parameters which need to be either estimated or considered when the location is estimated.
In this work, we exploit cooperative localization as a recent and trending technology and semidefinite programming (SDP) as a powerful tool in our research. Cooperative localization has several advantages over the traditional noncooperative localization in terms of positioning accuracy and localizability. Cooperation is also highly beneficial for networks with few anchor nodes and low communication range. On the other hand, SDP provides an alternative solution to the optimal maximumlikelihood (ML) estimation. Unlike in the ML estimator, convergence to the global minimum is guaranteed in SDP. It also has significantly lower complexity especially for cooperative networks in exchange for small performance degradation. Using these two concepts, four open problems within the area of cooperative localization and tracking in the presence of nuisance parameters are addressed. In particular, we focus on cooperative received signal strengthbased localization when the propagation parameters including pathloss exponent and transmit powers are unknown. Cooperative timeofarrivalbased localization in harsh environments in the presence of severe nonlineofsight (NLOS) propagation is also investigated. Cooperative localization in asynchronous networks is studied where the clock parameters are considered as nuisance parameters and the focus is on a joint synchronization and localization approach. Lastly, source tracking in NLOS environments is studied where source nodes are mobile and their status changes rapidly from LOS to NLOS and vice versa. / Ph. D.

2 
Mathematical Programming Formulations of the Planar Facility Location ProblemZvereva, Margarita January 2007 (has links)
The facility location problem is the task of optimally placing a
given number of facilities in a certain subset of the plane. In
this thesis, we present various mathematical programming
formulations of the planar facility location problem, where
potential facility locations are not specified. We first consider
mixedinteger programming formulations of the planar facility
locations problems with squared Euclidean and rectangular distance
metrics to solve this problem to provable optimality. We also
investigate a heuristic approach to solving the problem by extending
the $K$means clustering algorithm and formulating the facility
location problem as a variant of a semidefinite programming problem,
leading to a relaxation algorithm. We present computational results
for the mixedinteger formulations, as well as compare the objective
values resulting from the relaxation algorithm and the modified
$K$means heuristic. In addition, we briefly discuss some of the
practical issues related to the facility location model under the
continuous customer distribution.

3 
A Semidefinite Programming Model for the Facility Layout ProblemAdams, Elspeth January 2010 (has links)
The continuous facility layout problem consists of arranging a set of facilities so that no pair overlaps and the total sum of the pairwise connection costs (proportional to the centertocenter rectilinear distance) is minimized. This thesis presents a completely mixed integer semidefinite programming (MISDP) model for the continuous facility layout problem.
To begin we describe the problem in detail; discuss the conditions required for a feasible layout; and define quaternary variables. These variables are the basis of the MISDP model. We prove that the model is an exact formulation and a distinction is made between the constraints that semidefinite programming (SDP) optimization software can solve and those that must be relaxed. The latter are called exactness constraints and three possible exactness constraints are shown to be equivalent.
The main contribution of this thesis is the theoretical development of a MISDP model that is based on quaternary, as oppose to binary, variables; nevertheless preliminary computational results will be presented for problems with 5 to 20 facilities. The optimal solution is found for problems with 5 and 6 facilities, confirming the validity of the model; and the potential of the model is revealed as a new upper bound is found for an 11facility problem.

4 
Linear phase filter bank design by convex programmingHa, Hoang Kha, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW January 2008 (has links)
Digital filter banks have found in a wide variety of applications in data compression, digital communications, and adaptive signal processing. The common objectives of the filter bank design consist of frequency selectivity of the individual filters and perfect reconstruction of the filter banks. The design problems of filter banks are intrinsically challenging because their natural formulations are nonconvex constrained optimization problems. Therefore, there is a strong motivation to cast the design problems into convex optimization problems whose globally optimal solutions can be efficiently obtained. The main contributions of this dissertation are to exploit the convex optimization algorithms to design several classes of the filter banks. First, the twochannel orthogonal symmetric complexvalued filter banks are investigated. A key contribution is to derive the necessary and sufficient condition for the existence of complexvalued symmetric spectral factors. Moreover, this condition can be expressed as linear matrix inequalities (LMIs), and hence semidefinite programming (SDP) is applicable. Secondly, for twochannel symmetric realvalued filter banks, a more general and efficient method for designing the optimal triplet halfband filter banks with regularity is developed. By exploiting the LMI characterization of nonnegative cosine polynomials, the semiinfinite constraints can be efficiently handled. Consequently, the filter bank design is cast as an SDP problem. Furthermore, it is demonstrated that the resulting filter banks are applied to image coding with improved performance. It is not straightforward to extend the proposed design methods for twochannel filter banks to Mchannel filter banks. However, it is investigated that the design problem of Mchannel cosinemodulated filter banks is a nonconvex optimization problem with the low degree of nonconvexity. Therefore, the efficient semidefinite relaxation technique is proposed to design optimal prototype filters. Additionally, a cheap iterative algorithm is developed to further improve the performance of the filter banks. Finally, the application of filter banks to multicarrier systems is considered. The condition on the transmit filter bank and channel for the existence of zeroforcing filter bank equalizers is obtained. A closedform expression of the optimal equalizer is then derived. The proposed filter bank transceivers are shown to outperform the orthogonal frequencydivision multiplexing (OFDM) systems.

5 
Mathematical Programming Formulations of the Planar Facility Location ProblemZvereva, Margarita January 2007 (has links)
The facility location problem is the task of optimally placing a
given number of facilities in a certain subset of the plane. In
this thesis, we present various mathematical programming
formulations of the planar facility location problem, where
potential facility locations are not specified. We first consider
mixedinteger programming formulations of the planar facility
locations problems with squared Euclidean and rectangular distance
metrics to solve this problem to provable optimality. We also
investigate a heuristic approach to solving the problem by extending
the $K$means clustering algorithm and formulating the facility
location problem as a variant of a semidefinite programming problem,
leading to a relaxation algorithm. We present computational results
for the mixedinteger formulations, as well as compare the objective
values resulting from the relaxation algorithm and the modified
$K$means heuristic. In addition, we briefly discuss some of the
practical issues related to the facility location model under the
continuous customer distribution.

6 
A Semidefinite Programming Model for the Facility Layout ProblemAdams, Elspeth January 2010 (has links)
The continuous facility layout problem consists of arranging a set of facilities so that no pair overlaps and the total sum of the pairwise connection costs (proportional to the centertocenter rectilinear distance) is minimized. This thesis presents a completely mixed integer semidefinite programming (MISDP) model for the continuous facility layout problem.
To begin we describe the problem in detail; discuss the conditions required for a feasible layout; and define quaternary variables. These variables are the basis of the MISDP model. We prove that the model is an exact formulation and a distinction is made between the constraints that semidefinite programming (SDP) optimization software can solve and those that must be relaxed. The latter are called exactness constraints and three possible exactness constraints are shown to be equivalent.
The main contribution of this thesis is the theoretical development of a MISDP model that is based on quaternary, as oppose to binary, variables; nevertheless preliminary computational results will be presented for problems with 5 to 20 facilities. The optimal solution is found for problems with 5 and 6 facilities, confirming the validity of the model; and the potential of the model is revealed as a new upper bound is found for an 11facility problem.

7 
Linear phase filter bank design by convex programmingHa, Hoang Kha, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW January 2008 (has links)
Digital filter banks have found in a wide variety of applications in data compression, digital communications, and adaptive signal processing. The common objectives of the filter bank design consist of frequency selectivity of the individual filters and perfect reconstruction of the filter banks. The design problems of filter banks are intrinsically challenging because their natural formulations are nonconvex constrained optimization problems. Therefore, there is a strong motivation to cast the design problems into convex optimization problems whose globally optimal solutions can be efficiently obtained. The main contributions of this dissertation are to exploit the convex optimization algorithms to design several classes of the filter banks. First, the twochannel orthogonal symmetric complexvalued filter banks are investigated. A key contribution is to derive the necessary and sufficient condition for the existence of complexvalued symmetric spectral factors. Moreover, this condition can be expressed as linear matrix inequalities (LMIs), and hence semidefinite programming (SDP) is applicable. Secondly, for twochannel symmetric realvalued filter banks, a more general and efficient method for designing the optimal triplet halfband filter banks with regularity is developed. By exploiting the LMI characterization of nonnegative cosine polynomials, the semiinfinite constraints can be efficiently handled. Consequently, the filter bank design is cast as an SDP problem. Furthermore, it is demonstrated that the resulting filter banks are applied to image coding with improved performance. It is not straightforward to extend the proposed design methods for twochannel filter banks to Mchannel filter banks. However, it is investigated that the design problem of Mchannel cosinemodulated filter banks is a nonconvex optimization problem with the low degree of nonconvexity. Therefore, the efficient semidefinite relaxation technique is proposed to design optimal prototype filters. Additionally, a cheap iterative algorithm is developed to further improve the performance of the filter banks. Finally, the application of filter banks to multicarrier systems is considered. The condition on the transmit filter bank and channel for the existence of zeroforcing filter bank equalizers is obtained. A closedform expression of the optimal equalizer is then derived. The proposed filter bank transceivers are shown to outperform the orthogonal frequencydivision multiplexing (OFDM) systems.

8 
Approximation Algorithms for MAX SATONO, Takao, HIRATA, Tomio 20 March 2000 (has links)
No description available.

9 
Semidefinite programming, binary codes and a graph coloring problemLi, Chao 29 May 2015 (has links)
"Experts in information theory have long been interested in the maximal size, A(n, d), of a binary errorcorrecting code of length n and minimum distance d, The problem of determining A(n, d) involves both the construction of good codes and the search for good upper bounds. For quite some time now, Delsarte's linear programming approach has been the dominant approach to obtaining the strongest general purpose upper bounds on the efficiency of errorcorrecting codes. From 1973 forward, the linear programming bound found many applications, but there were few significant theoretical advances until Schrijver proposed a new code upper bound via semidefinite programming in 2003. Using the Terwilliger algebra, a recently introduced extension of the BoseMesner algebra, Schrijver formulated a new SDP strengthening of the LP approach. In this project we look at the dual solutions of the semidefinite programming bound for binary errorcorrecting codes. We explore the combinatorial meaning of these variables for small n and d, such as n = 4 and d = 2. To obtain information like this, we wrote a computer program with both Matlab and CVX modules to get solution of our primal SDP formulation. Our program efficiently generates the primal solutions with corresponding constraints for any n and d. We also wrote a program in C++ to parse the output of the primal SDP problem, and another Matlab script to generate the dual SDP problem, which could be used in assigning combinatorial meaning to the values given in the dual optimal solution. Our code not only computes both the primal and dual optimal variable values, but allows the researcher to display them in meaningful ways and to explore their relationship and dependence on arameters. These values are expected to be useful for later study of the combinatorial meaning of such solutions."

10 
Sensor network localization via Schatten QuasiNorm minimization: an interiorpoint approach. / CUHK electronic theses & dissertations collectionJanuary 2013 (has links)
Sze, Kam Fung. / Thesis (M.Phil.)Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 4953). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

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