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Optimization of SOC Sub-Circuits Using Mathematical Modeling
Published in Durgesh Nandan, Basant K. Mohanty, Sanjeev Kumar, Rajeev Kumar Arya, VLSI Architecture for Signal, Speech, and Image Processing, 2023
Mathematical attributes of convex optimization [51] and geometric programming [52] have been practiced and appreciated for decades. Convex optimization techniques concerning the minimization of convex functions over convex sets are simpler than the general optimization methods, since global minimum replaces local minimum. However, practical applications of these methodologies have started seeing broad daylight only after the deployment of interior-point algorithms. They are ideally suited for larger problems. Regardless to the primary settings, these techniques can achieve a global optimum outcome with unprecedented efficiency. Another merit of is that if the design requirements are too tight to be complied simultaneous, i.e., if they are mutually inconsistent, then the program explicitly reports the same by raising a flag. Also, due to the absence of ‘learning modules,’ there is no unnecessary delay in the execution process.
Challenges and Opportunities of Machine Learning and Deep Learning Techniques for the Internet of Drones
Published in Arun Solanki, Sandhya Tarar, Simar Preet Singh, Akash Tayal, The Internet Of Drones, 2023
Roshan Lal, Sandhya Tarar, Chilamkurti Naveen Smieee
Optimization: The way candidate programs are generated. Examples:Combinatorial optimization;Convex optimization;Constraint optimization.
Compressive Sensing Fundamentals
Published in Moeness Amin, Compressive Sensing for Urban Radar, 2017
When x is real valued, BP can be cast as a linear program. When x is complex valued, BP can be cast as a second-order cone program (SOCP). Standard techniques from convex optimization, such as the simplex method or interior point methods, can be used for solving these problems [27]. Popular software packages include ℓ1-MAGIC [39] (for solving a particular set of sparse recovery problems) and CVX [98,99] (for solving general convex optimization problems of modest size). For BP, ℓ1-MAGIC is restricted to real-valued vectors x, while CVX can be used for real-valued vectors or, if declared as such, complex-valued vectors.
Optimal control method of active distribution network considering soft open point and thermostatically controlled loads under distributed photovoltaic access
Published in Systems Science & Control Engineering, 2023
Lisheng Li, Haidong Yu, Yang Liu, Wenbin Liu, Min Huang, Pengping Zhang, Xinhong You, Shuai Li
Except for Eqs. (2), (3), (12), (16), and (17), all constraints in the distribution network reconfiguration model and the SOP mathematical model are linear. Eqs. (2), (3), (12), (16), and (17) are non-linear constraints with strong non-convexity. This model must take into account the switching state of the branch, the operating state of the electric water heater, and so on. It is a mixed integer non-linear programming (MINLP) model. In addition, the constraints shown in Eq. (11) are only for closed branches and do not consider the effect of branch opening and closing on the distribution network power flow distribution, which cannot be used in distribution network reconfiguration optimization. In this paper, the Big-M method is used to perform the relaxation transformation of Eq. (11), and on this basis, use the second-order cone optimization algorithm based on the mathematical optimization algorithm (Liu et al., 2014) to perform the SOCR for Eqs. (2), (3), (12), (16), and (17) to transform the MINLP problem into the MISOCP. The convex optimization problem can be solved quickly using commercial solvers such as CPELX and GUROBI. Distribution network power flow constraints transformation
Network resource optimization configuration in edge computing environment
Published in International Journal of Computers and Applications, 2023
Yong Liu, Jiabao Jiang, Yun Liu, Yong Zhang, Qilin Wu
Convex optimization is an important branch of optimization problem, which is widely used in signal processing, communication networks, circuit design, data analysis and modeling, statistics and so on. The convex optimization problem refers to minimizing a convex objective function under convex constraints. One problem is convex optimization problem or can be described as convex optimization problem. It is very convenient to solve. The most essential benefit is convex optimization problem. The local optimal value is also the global optimal value, which can be solved quickly and accurately by the interior point method or other convex optimization methods. These solving methods are reliable enough to make the convex optimization technique can be embedded in computer-aided design or analysis tools in engineering applications.
Painlevé–Kuratowski convergences of the solution sets for set optimization problems with cone-quasiconnectedness
Published in Optimization, 2022
In a general way, non-convex optimization problems are more difficult to solve than convex optimization problems, since the tools in convex analysis are hard to deal with non-convex optimization problems. We note that, in the work of [11, 12, 14–17], the convexity of the objective mapping plays an important role in establishing the stability of the solution sets for set optimization problems. Therefore, it is important and interesting to study the stability of the solution sets for set optimization problems without the convexity of the objective mapping. The first aim of this paper is to make an attempt in this direction. In this paper, we introduce the concepts of cone-quasiconnectedness and strictly cone-quasiconnectedness for set-valued mappings and then we establish the Painlevé–Kuratowski convergences of the solution sets for set optimization problems. On the other hand, it is worth to mention that the authors in [9, 16, 17] do not discuss the stability of the solution sets for set optimization problems with respect to the perturbation of the objective mapping. Therefore, it is natural to understand whether we can obtain the stability of the solution sets for set optimization problems with respect to the perturbation of the objective mapping. The second aim of this paper is to establish the Painlevé–Kuratowski convergence of the solution sets for set optimization problems with respect to the perturbation of the objective mapping by using a new convergence for the sequence of set-valued mappings.