Browsing by Subject "Parameter spaces"

Now showing 1 - 3 of 3

Open Access
A new OMP technique for sparse recovery
(IEEE, 2012) Teke, Oğuzhan; Gürbüz, A.C.; Arıkan, Orhan
Compressive Sensing (CS) theory details how a sparsely represented signal in a known basis can be reconstructed using less number of measurements. However in reality there is a mismatch between the assumed and the actual bases due to several reasons like discritization of the parameter space or model errors. Due to this mismatch, a sparse signal in the actual basis is definitely not sparse in the assumed basis and current sparse reconstruction algorithms suffer performance degradation. This paper presents a novel orthogonal matching pursuit algorithm that has a controlled perturbation mechanism on the basis vectors, decreasing the residual norm at each iteration. Superior performance of the proposed technique is shown in detailed simulations. © 2012 IEEE.
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A parametric simplex algorithm for linear vector optimization problems
(Springer, 2017) Rudloff, B.; Ulus, F.; Vanderbei, R.
In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (the Evans–Steuer) algorithm (Math Program 5(1):54–72, 1973). Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Löhne (Vector optimization with infimum and supremum. Springer, Berlin, 2011), that is, it finds a subset of efficient solutions that allows to generate the whole efficient frontier. In that sense, it can also be seen as a generalization of the parametric self-dual simplex algorithm, which originally is designed for solving single objective linear optimization problems, and is modified to solve two objective bounded LVOPs with the positive orthant as the ordering cone in Ruszczyński and Vanderbei (Econometrica 71(4):1287–1297, 2003). The algorithm proposed here works for any dimension, any solid pointed polyhedral ordering cone C and for bounded as well as unbounded problems. Numerical results are provided to compare the proposed algorithm with an objective space based LVOP algorithm [Benson’s algorithm in Hamel et al. (J Global Optim 59(4):811–836, 2014)], that also provides a solution in the sense of Löhne (2011), and with the Evans–Steuer algorithm (1973). The results show that for non-degenerate problems the proposed algorithm outperforms Benson’s algorithm and is on par with the Evans–Steuer algorithm. For highly degenerate problems Benson’s algorithm (Hamel et al. 2014) outperforms the simplex-type algorithms; however, the parametric simplex algorithm is for these problems computationally much more efficient than the Evans–Steuer algorithm. © 2016, Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.
Open Access
Simulation optimization: a comprehensive review on theory and applications
(Taylor & Francis, 2004) Tekin, E.; Sabuncuoglu, I.
For several decades, simulation has been used as a descriptive tool by the operations research community in the modeling and analysis of a wide variety of complex real systems. With recent developments in simulation optimization and advances in computing technology, it now becomes feasible to use simulation as a prescriptive tool in decision support systems. In this paper, we present a comprehensive survey on techniques for simulation optimization with emphasis given on recent developments. We classify the existing techniques according to problem characteristics such as shape of the response surface (global as compared to local optimization), objective functions (single or multiple objectives) and parameter spaces (discrete or continuous parameters). We discuss the major advantages and possible drawbacks of the different techniques. A comprehensive bibliography and future research directions are also provided in the paper.