Topic
Convex optimization
About: Convex optimization is a research topic. Over the lifetime, 24906 publications have been published within this topic receiving 908795 citations. The topic is also known as: convex optimisation.
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TL;DR: In the paper, the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory (BAM) neural networks of neutral type by using the Lyapunov method in terms of linear matrix inequality (LMI).
188 citations
TL;DR: Comparisons with other classes of Lyapunov functions through numerical examples taken from the literature show that HPLFs are a powerful tool for robustness analysis.
187 citations
TL;DR: Numerical experiments show that the solutions to the sequence of convex programs converge to the same design point for widely varying initial guesses, suggesting that the approach is capable of determining the globally optimal solution to the CMOS op-amp circuit sizing problem.
Abstract: The problem of CMOS op-amp circuit sizing is addressed here. Given a circuit and its performance specifications, the goal is to automatically determine the device sizes in order to meet the given performance specifications while minimizing a cost function, such as a weighted sum of the active area and power dissipation. The approach is based on the observation that the first order behavior of a MOS transistor in the saturation region is such that the cost and the constraint functions for this optimization problem can be modeled as posynomial in the design variables. The problem is then solved efficiently as a convex optimization problem. Second order effects are then handled by formulating the problem as one of solving a sequence of convex programs. Numerical experiments show that the solutions to the sequence of convex programs converge to the same design point for widely varying initial guesses. This strongly suggests that the approach is capable of determining the globally optimal solution to the problem. Accuracy of performance prediction in the sizing program (implemented in MATLAB) is maintained by using a newly proposed MOS transistor model and verified against detailed SPICE simulation.
187 citations
TL;DR: This work designs a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors by using the alternating direction method of multipliers (ADMM).
Abstract: We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks.
187 citations
TL;DR: An algebraic characterization of the feasible region in a higher-dimensional space is derived and a solution procedure akin to the interior-point approach for convex programming is proposed.
Abstract: Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of finding the minimum of a convex function on the closure of the convex hull of the union of those sets. We derive an algebraic characterization of the feasible region in a higher-dimensional space and propose a solution procedure akin to the interior-point approach for convex programming.
187 citations