Browsing by Subject "Quadratic programming"

Now showing 1 - 6 of 6

Open Access
Automatic detection of compound structures by joint selection of region groups from multiple hierarchical segmentations
(2016-09) Akçay, Hüseyin Gökhan
A challenging problem in remote sensing image interpretation is the detection of heterogeneous compound structures such as different types of residential, industrial, and agricultural areas that are comprised of spatial arrangements of simple primitive objects such as buildings and trees. We describe a generic method for the modeling and detection of compound structures that involve arrangements of unknown number of primitives appearing in different primitive object layers in large scenes. The modeling process starts with example structures, considers the primitive objects as random variables, builds a contextual model of their arrangements using a Markov random field, and learns the parameters of this model via sampling from the corresponding maximum entropy distribution. The detection task is reduced to the selection of multiple subsets of candidate regions from multiple hierarchical segmentations corresponding to different primitive object layers where each set of selected regions constitutes an instance of the example compound structures. The combinatorial selection problem is solved by joint sampling of groups of regions by maximizing the likelihood of their individual appearances and relative spatial arrangements under the model learned from the example structures of interest. Moreover, we incorporate linear equality and inequality constraints on the candidate regions to prevent the co-selection of redundant overlapping regions and to enforce a particular spatial layout that must be respected by the selected regions. The constrained selection problem is formulated as a linearly constrained quadratic program that is solved via a variant of the primal-dual algorithm called the Difference of Convex algorithm by rewriting the non-convex program as the difference of two convex programs. Extensive experiments using very high spatial resolution images show that the proposed method can provide good localization of unknown number of instances of different compound structures that cannot be detected by using spectral and shape features alone.
Open Access
Comparison of the formulations for a hub-and-spoke network design problem under congestion
(Elsevier, 2016) Kian, Ramer; Kargar, Kamyar
In this paper, we study the hub location problem with a power-law congestion cost and propose an exact solution approach. We formulate this problem in a conic quadratic form and use a strengthening method which rests on valid inequalities of perspective cuts in mixed integer nonlinear programming. In a numerical study, we compare two well known types of mathematical modeling in the hub-location problems which are solved with different branch and cut strategies. The strength and weakness of the formulations are summarized based on an extensive numerical study over the CAB data set. © 2016 Elsevier Ltd
Open Access
Duality in robust linear regression using Huber's M-estimator
(Elsevier, 1997-07) Pınar, M. Ç.
The robust linear regression problem using Huber's piecewise-quadratic M-estimator function is considered. Without exception, computational algorithms for this problem have been primal in nature. In this note, a dual formulation of this problem is derived using Lagrangean duality. It is shown that the dual problem is a strictly convex separable quadratic minimization problem with linear equality and box constraints. Furthermore, the primal solution (Huber's M-estimate) is obtained as the optimal values of the Lagrange multipliers associated with the dual problem. As a result, Huber's M-estimate can be computed using off-the-shelf optimization software.
Open Access
FIR filter design by iterative convex relaxations with rank refinement
(IEEE, 2014) Dedeoğlu, Mehmet; Alp, Yaşar Kemal; Arıkan, Orhan
Finite impulse response (FIR) filters have been a primary topic of digital signal processing since their inception. Although FIR filter design is an old problem, with the developments of fast convex solvers, convex modelling approach for FIR filter design has become an active research topic. In this work, we propose a new method based on convex programming for designing FIR filters with the desired frequency characteristics. FIR filter design problem, which is modelled as a non-convex quadratically constrained quadratic program (QCQP), is transformed to a semidefinite program (SDP). By relaxing the constraints, a convex programming problem, which we call RSDP(Relaxed Semidefinite Program), is obtained. Due to the relaxation, solution to the RSDPs fails to be rank-1. Typically used rank-1 approximations to the obtained RSDP solution does not satisfy the constraints. To overcome this issue, an iterative algorithm is proposed, which provides a sequence of solutions that converge to a rank-1 matrix. Conducted experiments and comparisons demonstrate that proposed method successfully designs FIR filters with highly flexible frequency characteristics.
Open Access
Portfolio selection methods: an application to Istanbul Securities Exchange Market
(1991) Tuntaş, Mustafa Cem
In this study, frequently used Portfolio Theories are described and The Markowitz Mean Variance Model is used for the construction of the efficient frontier. In the construction of the efficient frontier daily price data from Istanbul Securities Exchange Market's First Market stocks during January 1 1990 - January 1 1991 period is used and the method is found useful for the ones who do not have insider information.
Open Access
A saturated linear dynamical network for approximating maximum clique
(Institute of Electrical and Electronics Engineers, 1999-06) Pekergin, F.; Morgül, Ö.; Güzeliş, C.
We use a saturated linear gradient dynamical network for finding an approximate solution to the maximum clique problem. We show that for almost all initial conditions, any solution of the network defined on a closed hypercube reaches one of the vertices of the hypercube, and any such vertex corresponds to a maximal clique. We examine the performance of the method on a set of random graphs and compare the results with those of some existing methods. The proposed model presents a simple continuous, yet powerful, solution in approximating maximum clique, which may outperform many relatively complex methods, e.g., Hopfield-type neural network based methods and conventional heuristics.