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Game Approach to Robust Sensor Location Estimation Problem in Wireless Sensor Networks
Published in Bor-Sen Chen, Stochastic Game Strategies and Their Applications, 2019
which is convex and can be solved by interior-point methods [221]. The physical meaning of SOCP method in (11.32) can be readily understood by replacing all inequality constraints with equality constraints. The relaxation of feasible solutions, i.e., using inequality constraints rather than equality constraints, transforms the problem into a convex SOCP, which is solvable with existing solvers. However, it is known that this relaxation can result in a “convex-hull” problem [217]. In particular, the performance can severely degrade if location-unaware sensors mostly lie outside the convex hull of zˆm, m=1,2,…,M. Therefore, a good deployment of sensors is needed for a good performance of SOCP method, for example, location-aware nodes positioned on the edges or vertices of the region monitored.
Optimization Techniques for Circuit Design Applications
Published in Charles J. Alpert, Dinesh P. Mehta, Sachin S. Sapatnekar, Handbook of Algorithms for Physical Design Automation, 2008
To recognize convex optimization problems in engineering applications, one must first be familiar with the basic concepts of convexity and the commonly used convex optimization models. This chapter starts with a concise review of these optimization concepts and models including linear programming, second-order cone programming (SOCP), semidefinite cone programming, as well as geometric programming, all illustrated through concrete examples. In addition, the Karush–Kuhn–Tucker optimality conditions are reviewed and stated explicitly for each of the convex optimization models, followed by a description of the well-known interior point algorithms and a brief discussion of their worst-case complexity. The chapter concludes with an example illustrating the use of robust optimization techniques for a circuit design problem under process variations.
Radio Resources Management Optimization in Cognitive Radio Networks
Published in Athanasios G. Kanatas, Konstantina S. Nikita, Panagiotis Mathiopoulos, New Directions in Wireless Communications Systems, 2017
Anargyros J. Roumeliotis, Marios I. Poulakis, Stavroula Vassaki, Athanasios D. Panagopoulos
Another class of convex optimization problems is the second order cone programs (SOCP) that involves conic expressions under continuous optimization variables and its formal structure is (Boyd et al., 2004): () minimize xfTxsubjectto‖Aix+b‖2≤ciTx+di,i=1,…,mFx=g
Numerical study on the bearing capacity of strip footing resting on partially saturated soil subjected to combined vertical-horizontal-moment loading
Published in European Journal of Environmental and Civil Engineering, 2023
Hessam Fathipour, Meghdad Payan, Amirhossein Safardoost Siahmazgi, Reza Jamshidi Chenari, Kostas Senetakis
Ergo, the amount of ultimate failure load (), horizontal load () and moment () are calculated as and respectively. The primal-dual interior-point algorithm (after Andersen et al., 2003) is used to perform the SOCP optimization (Makrodimopoulos & Martin, 2006). It is worth noting that the implementation of the primal-dual interior-point algorithm for solving second-order cone optimization is based on a homogeneous and self-dual model, which handles rotated quadratic cones directly, and employs a Mehrotra type predictor-corrector extension and sparse linear algebra to improve the computational efficiency (Andersen et al., 2003). A detailed computational procedure followed in the course of this study is demonstrated in the flowchart in Figure 5 (Fathipour et al., 2020, 2021a, 2021b, 2021c, 2022; Safardoost Siahmazgi et al., 2021; Sloan, 1988, 2013; Tang et al., 2015).
Classifying random variables based on support vector machine and a neural network scheme
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2022
During several years, there are various studies on SVM under uncertainty. For example, Ben-Tal et al. (2011) displayed the new maximum-margin classification formulations that are robust to uncertainties in training data. In many studies, probabilistic–constrained problem be converted into an SOCP (Lobo et al., 1998) that can be solved by the interior point method (IPM; Mehrotra, 1992). For example, Shivaswamy et al. (2006) proposed an SOCP formulation for designing robust linear prediction function which are capable of tackling uncertainty in the pattern in classification setting. Generally, solving an SOCP is more difficult than solving QP. Park and Kil (2009) presented a new method of postprocessing for the probabilistic scaling of classifier’s output.
A joint TDOA and FDOA estimation algorithm based on second-order cone programming
Published in International Journal of Electronics, 2019
Z. X. Liu, D. X. Hu, Y. J. Zhao
Based on the above facts, a quadratic surface interpolation algorithm for joint TDOA and FDOA estimation is proposed in this paper. It should be noted that this paper uses three assumptions: 1) approximate the TDOA and FDOA as constant parameters over the correlation acquisition time (Tao et al., 2008; Palmer et al., 2011; Zhang, Li, Liu, & Himed, 2016); 2) Negligible Doppler distortions of the modulation function (Rihaczek., 2010); 3) Negligible effects of range acceleration and higher-order range derivatives (Rihaczek, 2010). These assumptions, respectively, ensure that the source does not happen the range migration in time domain and range-Doppler domain during the acquisition time. Specific ideas of the proposed method are listed as follows: Firstly, the convex optimization models with regard to interpolation surface function are built by using generalized extended approximation (GEA) method. Then, the interpolation surface is achieved by second-order cone programming (SOCP) (Liu, Hu, Zhao, & Liu, 2016; Sturm., 1999). Finally, the estimation results of two positioning parameters including TDOA and FDOA can be determined through search for maximum of the interpolation surface. This algorithm includes both merits of ‘soft’ and ‘hard’ constraint. More specifically, the ‘soft’ constraint means minimizing the distance between surface points and original points as close as possible. The ‘hard’ constraint is built to make the surface points equal to original point. It is efficient to reduce the estimation variance of interpolation algorithms. In addition, due to the high accuracy, fast convergence, excellent operability and reasonable computational complexity of SOCP (Liu et al., 2016; Sturm, 1999), we use this tool to solve the convex optimization models.