scholarly journals Beyond convex relaxation: A polynomial-time non-convex optimization approach to network localization

2013 ◽  
Author(s):  
Senshan Ji ◽  
Kam-Fung Sze ◽  
Zirui Zhou ◽  
Anthony Man-Cho So ◽  
Yinyu Ye
Keyword(s):  
Convex Optimization ◽  
Polynomial Time ◽  
Convex Relaxation ◽  
Optimization Approach ◽  
Network Localization

scholarly journals A Convex Optimization Approach for the Design of Supergain Electrically Small Antenna and Rectenna Arrays Comprising Parasitic Reactively Loaded Elements

2021 ◽  
Author(s):  
Apostolos Georgiadis ◽  
Nuno Borges Carvalho
Keyword(s):  
Convex Optimization ◽  
Antenna Arrays ◽  
Convex Relaxation ◽  
Linear Constraints ◽  
Optimization Approach ◽  
Quadratic Constraints ◽  
Electrically Small Antenna ◽  
Optimization Formulation ◽  
Small Antenna ◽  
Array Gain

<div><div><div><p>A convex optimization formulation is provided for antenna arrays comprising reactively loaded parasitic elements. The objective function consists of maximizing the array gain, while constraints on the admittance are provided in order to properly account for reactive loads. Topologies with two and three electrically small dipole arrays comprising one fed element and one or two parasitic elements respectively are considered and the conditions for obtaining supergain are investigated. The admittance constraints are formulated as linear constraints for specific cases as well as more general, quadratic constraints, which lead to the solution of an equivalent convex relaxation formulation. A design example for an electrically small superdirective rectenna is provided where an upper bound for the rectifier efficiency is simulated.</p></div></div></div>

scholarly journals A Convex Optimization Approach for the Design of Supergain Electrically Small Antenna and Rectenna Arrays Comprising Parasitic Reactively Loaded Elements

2021 ◽  
Author(s):  
Apostolos Georgiadis ◽  
Nuno Borges Carvalho
Keyword(s):  
Convex Optimization ◽  
Antenna Arrays ◽  
Convex Relaxation ◽  
Linear Constraints ◽  
Optimization Approach ◽  
Quadratic Constraints ◽  
Electrically Small Antenna ◽  
Optimization Formulation ◽  
Small Antenna ◽  
Array Gain

<div><div><div><p>A convex optimization formulation is provided for antenna arrays comprising reactively loaded parasitic elements. The objective function consists of maximizing the array gain, while constraints on the admittance are provided in order to properly account for reactive loads. Topologies with two and three electrically small dipole arrays comprising one fed element and one or two parasitic elements respectively are considered and the conditions for obtaining supergain are investigated. The admittance constraints are formulated as linear constraints for specific cases as well as more general, quadratic constraints, which lead to the solution of an equivalent convex relaxation formulation. A design example for an electrically small superdirective rectenna is provided where an upper bound for the rectifier efficiency is simulated.</p></div></div></div>

scholarly journals Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

2014 ◽  
Vol 11 (100) ◽  
pp. 20140713 ◽  
Author(s):  
Gilad Poker ◽  
Yoram Zarai ◽  
Michael Margaliot ◽  
Tamir Tuller
Keyword(s):  
Synthetic Biology ◽  
Convex Optimization ◽  
Production Rate ◽  
Protein Production ◽  
Flow Model ◽  
Protein Translation ◽  
Optimization Approach ◽  
Initiation Rate ◽  
Translation Rate ◽  
Protein Production Rate

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation–elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n . Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.

scholarly journals A Sparse Optimization Approach for Energy-Efficient Timetabling in Metro Railway Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Ziyan Luo ◽  
Xiaoyu Li ◽  
Naihua Xiu
Keyword(s):  
Optimization Model ◽  
Energy Efficient ◽  
Convex Relaxation ◽  
Sparse Optimization ◽  
Computational Time ◽  
Optimization Approach ◽  
Railway Systems ◽  
Alternating Direction ◽  
Np Hard Problem ◽  
Regenerative Energy

In this paper, we propose a sparse optimization approach to maximize the utilization of regenerative energy produced by braking trains for energy-efficient timetabling in metro railway systems. By introducing the cardinality function and the square of the Euclidean norm function as the objective function, the resulting sparse optimization model can characterize the utilization of the regenerative energy appropriately. A two-stage alternating direction method of multipliers is designed to efficiently solve the convex relaxation counterpart of the original NP-hard problem and then to produce an energy-efficient timetable of trains. The resulting approach is applied to Beijing Metro Yizhuang Line with different instances of service for case study. Comparison with the existing two-step linear program approach is also conducted which illustrates the effectiveness of our proposed sparse optimization model in terms of the energy saving rate and the efficiency of our numerical optimization algorithm in terms of computational time.

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