Browsing by Subject "Cost functions"

Now showing 1 - 11 of 11

Open Access
Consensus as a Nash equilibrium of a dynamic game
(IEEE, 2016) Niazi, Muhammad Umar B.; Özgüler, Arif Bülent; Yıldız, Aykut
Consensus formation in a social network is modeled by a dynamic game of a prescribed duration played by members of the network. Each member independently minimizes a cost function that represents his/her motive. An integral cost function penalizes a member's differences of opinion from the others as well as from his/her own initial opinion, weighted by influence and stubbornness parameters. Each member uses its rate of change of opinion as a control input. This defines a dynamic non-cooperative game that turns out to have a unique Nash equilibrium. Analytic explicit expressions are derived for the opinion trajectory of each member for two representative cases obtained by suitable assumptions on the graph topology of the network. These trajectories are then examined under different assumptions on the relative sizes of the influence and stubbornness parameters that appear in the cost functions.
Open Access
Coordination of staffing and pricing decisions in a service firm
(John Wiley & Sons, 2008) Serel, D. A.; Erel, E.
Customer demand is sensitive to the price paid for the service in many service environments. Using queueing theory framework, we develop profit maximization models for jointly determining the price and the staffing level in a service company. The models include constraints on the average waiting time and the blocking probability. We show convexity of the single-variable subproblem under certain plausible assumptions on the demand and staffing cost functions. Using numerical examples, we investigate the sensitivity of the price and the staffing level to changes in the marginal service cost and the user-specified constraint on the congestion measure.
Open Access
Cross-term free based bistatic radar system using sparse least squares
(SPIE, 2015) Sevimli, R. Akın; Çetin, A. Enis
Passive Bistatic Radar (PBR) systems use illuminators of opportunity, such as FM, TV, and DAB broadcasts. The most common illuminator of opportunity used in PBR systems is the FM radio stations. Single FM channel based PBR systems do not have high range resolution and may turn out to be noisy. In order to enhance the range resolution of the PBR systems algorithms using several FM channels at the same time are proposed. In standard methods, consecutive FM channels are translated to baseband as is and fed to the matched filter to compute the range-Doppler map. Multichannel FM based PBR systems have better range resolution than single channel systems. However superious sidelobe peaks occur as a side effect. In this article, we linearly predict the surveillance signal using the modulated and delayed reference signal components. We vary the modulation frequency and the delay to cover the entire range-Doppler plane. Whenever there is a target at a specific range value and Doppler value the prediction error is minimized. The cost function of the linear prediction equation has three components. The first term is the real-part of the ordinary least squares term, the second-Term is the imaginary part of the least squares and the third component is the l2-norm of the prediction coefficients. Separate minimization of real and imaginary parts reduces the side lobes and decrease the noise level of the range-Doppler map. The third term enforces the sparse solution on the least squares problem. We experimentally observed that this approach is better than both the standard least squares and other sparse least squares approaches in terms of side lobes. Extensive simulation examples will be presented in the final form of the paper.
Open Access
Deconvolution using projections onto the epigraph set of a convex cost function
(IEEE, 2014) Tofighi, Mohammad; Bozkurt, Alican; Köse, K.; Çetin, A. Enis
A new deconvolution algorithm based on making orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and sets corresponding to the cost function and observations are defined. If the utilized cost function is convex in RN, the corresponding epigraph set is also convex in RN+1. The deconvolution algorithm starts with an arbitrary initial estimate in RN+1. At each iteration cycle of the algorithm, first deconvolution projections are performed onto the hyperplanes representing observations, then an orthogonal projection is performed onto epigraph of the cost function. The method provides globally optimal solutions for total variation, l1, l2, and entropic cost functions.
Open Access
Electromagnetic imaging of three-dimensional dielectric objects with Newton minimization
(IEEE, 2014) Etminan, Aslan; Sadeghi, Alireza; Gürel, Levent
We present a general framework for detecting the shape and electrical properties of unknown objects by using the Newton minimization approach for solving inverse-scattering problems. This procedure is performed by evolving an initial-guess object iteratively until the cost function decreases to a desired value. Rapid convergence of this method is demonstrated by some numerical results.
Open Access
Pasif bistatik radarlarda seyreklik temellli ters evrişim kullanılarak hedef tespiti
(IEEE, 2015-05) Arslan, Musa Tunç; Tofighi, Mohammad; Çetin, A. Enis
Bu bildiride pasif radar (PR) sistemlerinin menzil çözünürlüğünü artırmak için seyreklik tabanlı bir ters evrişim yöntemi sunulmaktadır. PR sistemlerinin iki boyutlu uyumlu süzgeç çıktısı bir ters evrişim problemli gibi düşünülerek incelenmektedir. Ters evrişim algoritması, hedeflerin zaman kaymaları ve l1 norm benzeri dışbükey maliyet fonksiyonlarının epigraf kümelerini temsil eden hiperdüzlemler üzerine izdüşümü temellidir. Bütün kısıt kümeleri kapalı ve dışbükey olduklarından dolayı yinelemeli algoritma yakınsamaktadır. FM tabanlı PR sistemleri üzerinde benzetim sonuçları sunulmuştur. Algoritma frekans uzayı tabanlı ters evrişim yöntemlerine göre daha yüksek performansa sahiptir.
Open Access
Projection-based wavelet denoising [lecture notes]
(Institute of Electrical and Electronics Engineers Inc., 2015) Çetin, A. Enis; Tofighi M.
In this lecture note, we describe a wavelet domain denoising method consisting of making orthogonal projections of wavelet (subbands) signals of the noisy signal onto an upside down pyramid-shaped region in a multidimensional space. Each horizontal slice of the upside down pyramid is a diamond shaped region and it is called an -ball. The upside down pyramid is called the epigraph set of the -norm cost function. We show that the method leads to soft-thresholding as in standard wavelet denoising methods. Orthogonal projection operations automatically determine the soft-threshold values of the wavelet signals. © 2015 IEEE.
Open Access
Projections onto convex sets (POCS) based optimization by lifting
(IEEE, 2013) Çetin, A. Enis; Bozkurt, Alican; Günay, Osman; Habiboglu, Yusuf Hakan; Köse, K.; Onaran, İbrahim; Tofighi, Mohammad; Sevimli, Rasim Akın
A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in R N+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p < 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems. © 2013 IEEE.
Open Access
Projections onto the epigraph set of the filtered variation function based deconvolution algorithm
(IEEE, 2017) Tofighi, M.; Çetin, A. Enis
A new deconvolution algorithm based on orthogonal projections onto the hyperplanes and the epigraph set of a convex cost function is presented. In this algorithm, the convex sets corresponding to the cost function are defined by increasing the dimension of the minimization problem by one. The Filtered Variation (FV) function is used as the convex cost function in this algorithm. Since the FV cost function is a convex function in RN, then the corresponding epigraph set is also a convex set in the lifted set in RN+1. At each step of the iterative deconvolution algorithm, starting with an arbitrary initial estimate in RN+1, first the projections onto the hyperplanes are performed to obtain the first deconvolution estimate. Then an orthogonal projection is performed onto the epigraph set of the FV cost function, in order to regularize and denoise the deconvolution estimate, in a sequential manner. The algorithm converges to the deblurred image.
Open Access
Shape reconstruction of three-dimensional conducting objects via near-field measurements
(IEEE, 2014) Etminan, Aslan; Gürel, Levent
A general framework for the shape reconstruction of conducting objects is presented with the Newton minimization approach. Using a fully numerical method, the initial-guess object is evolved to reconstruct the target. The object is modeled by triangles such that the vertices are the unknowns of the inverse-scattering problem. The cost function is minimized as the evolving object converges to the actual target in merely tens of iterations.
Open Access
Successive cancelation approach for doppler frequency estimation in pulse doppler radar systems
(IEEE, 2010) Soğancı, Hamza; Gezici, Sinan
In this paper, a successive cancelation approach is proposed to estimate Doppler frequencies of targets in pulse Doppler radar systems. This technique utilizes the Doppler domain waveform structure of the received signal coming from a point target after matched filtering and pulse Doppler processing steps. The proposed technique is an iterative algorithm. In each iteration, a target that minimizes a cost function is found, and the signal coming from that target is subtracted from the total received signal. These steps are repeated until there are no more targets. The global minimum value of the cost function in each iteration is found via particle swarm optimization (PSO). Performance of this technique is compared with the optimal maximum likelihood solution for various signal-to-noise ratio (SNR) values based on Monte Carlo simulations.