Convex Optimization Approach Research Articles

Stochastic Traffic assignment with Electric Vehicles: a convex optimization approach

Electric vehicles and charging stations are increasing worldwide to reduce emissions at the city level. In order to analyze traffic flows and quantify the demand for energy recharge, it is necessary to model users’ choices considering different kinds of traffic flows. In this paper, attention is focused on the formalization of the joint traffic and energy demand assignment conditions over a traffic network in presence of electric vehicles (EVs). Specifically, the so-called stochastic user equilibrium (SUE) conditions are used to define the steady state behaviour of a generic traffic network in which some arcs are equipped with EV charging stations. A convex optimization problem is defined and solved, which is equivalent to the solution of the nonlinear and nonconvex set of SUE conditions under a multinomial Logit user's choice function. A real case study, related to a touristic area in the Liguria Region (from Genova airport to Portofino), is considered.

Distributed Set-Membership Fusion Filtering for Nonlinear 2-D Systems Over Sensor Networks: An Encoding-Decoding Scheme.

In this article, the distributed set-membership fusion filtering problem is investigated for a class of nonlinear 2-D shift-varying systems subject to unknown-but-bounded noises over sensor networks. The sensors are communicated with their neighbors according to a given topology through wireless networks of limited bandwidth. With the purpose of relieving the communication burden as well as enhancing the transmission security, a logarithmic-type encoding-decoding mechanism is introduced for each sensor node so as to encode the transmitted data with a finite number of bits. A distributed set-membership filter is designed to determine the local ellipsoidal set that contains the system state by only utilizing the data from the local sensor node and its neighbors, where the proposed filter scheme is truly distributed with desirable scalability. Then, a new ellipsoid-based fusion rule is developed for the designed set-membership filters in order to form the fused ellipsoidal set that has a globally smaller volume than all local ellipsoidal sets. With the aid of the mathematical induction technique, the set theory, and the convex optimization approach, sufficient conditions are derived for the existence of the desired distributed set-membership filters and the fusion weights. Then, the filter parameters and the fusion weights are acquired by solving a set of constrained optimization problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed fusion filtering algorithm.

IRS-User Association in IRS-Aided MISO Wireless Networks: Convex Optimization and Machine Learning Approaches

This paper concentrates on the problem of associating an intelligent reflecting surface (IRS) to multiple users in a multiple-input single-output (MISO) downlink wireless communication network. The main objective of the paper is to maximize the sum-rate of all users by solving the joint optimization problem of the IRS-user association, IRS reflection, and BS beamforming, formulated as a non-convex mixed-integer optimization problem. The variable separation and relaxation are used to transform the problem into three convex sub-problems, which are alternatively solved through the convex optimization (CO) method. The major drawback of the proposed CO-based algorithm is high computational complexity. Thus, we make use of machine learning (ML) to tackle this problem. To this end, first, we convert the optimization problem into a regression problem. Then, we solve it with feed-forward neural networks (FNNs), trained by CO-based generated data. Simulation results show that the proposed ML-based algorithm has a performance equivalent to the CO-based algorithm, but with less computation complexity due to its offline training procedure.

A convex optimisation approach to parallel magnetic resonance imaging reconstruction

A convex optimisation approach to parallel magnetic resonance imaging reconstruction

A convex optimisation approach to parallel magnetic resonance imaging reconstruction

In parallel magnetic resonance imaging (pMRI), the image reconstruction with unknown coil sensitivity functions is known as a non-convex problem in the existing literatures. The analysis of this paper shows that there exists a convex solution region in the space of the magnitude image and sensitivity encoded image functions, which contains the true magnitude image solution. The derivation of the convex solution region resolves the non-convex difficulty and leads to a convex optimisation formulation of the pMRI reconstruction problem. The formulated problem consists of two steps. Each of the steps solves a regularised convex optimisation problem and provides a globally optimal solution, in the sense that the solution optimises the performance index and is independent of the initial conditions. The applications of the proposed two-step optimisation to in vivo and phantom data sets result in superior pMRI reconstruction performance compared with state-of-the-art algorithms.

An event-triggered iteratively reweighted convex optimization approach to multi-period portfolio selection

This paper addresses multi-period portfolio selection driven by events. We define an event-triggering function to mimic fund managers to activate sequential portfolio rebalancing and maximize Sharpe and Sortino ratios in the Markowitz’s return–risk framework. At first, the multi-period portfolio selection problem is formulated with a variable weight as a series of biconvex optimization problems with a surrogated objective function to maximize the Sharpe ratio or Sortino ratio. In each period, the portfolio optimization problem is further reformulated as an iteratively reweighted convex quadratic optimization problem. The multi-period portfolio selection problem is then solved sequentially based on a defined event-trigger function and a quadratic optimizer. The experiments are done on eight world stock markets datasets to show the capabilities of the proposed approach in calculating market indices and equal-weighted portfolios in terms of Sharpe and Sortino ratios.

Perception, Path Planning, and Flight Control for a Drone-Enabled Autonomous Pollination System

The decline of natural pollinators necessitates the development of novel pollination technologies. In this work, we propose a drone-enabled autonomous pollination system (APS) that consists of five primary modules: environment sensing, flower perception, path planning, flight control, and pollination mechanisms. These modules are highly dependent upon each other, with each module relying on inputs from the other modules. In this paper, we focus on approaches to the flower perception, path planning, and flight control modules. First, we briefly introduce a flower perception method from our previous work to create a map of flower locations. With a map of flowers, APS path planning is defined as a variant of the Travelling Salesman Problem (TSP). Two path planning approaches are compared based on mixed-integer programming (MIP) and genetic algorithms (GA), respectively. The GA approach is chosen as the superior approach due to the vast computational savings with negligible loss of optimality. To accurately follow the generated path for pollination, we develop a convex optimization approach to the quadrotor flight control problem (QFCP). This approach solves two convex problems. The first problem is a convexified three degree-of-freedom QFCP. The solution to this problem is used as an initial guess to the second convex problem, which is a linearized six degree-of-freedom QFCP. It is found that changing the objective of the second convex problem to minimize the deviation from the initial guess provides improved physical feasibility and solutions similar to a general-purpose optimizer. The path planning and flight control approaches are then tested within a model predictive control (MPC) framework where significant computational savings and embedded adjustments to uncertainty are observed. Coupling the two modules together provides a simple demonstration of how the entire APS will operate in practice.

Inverse linear-quadratic discrete-time finite-horizon optimal control for indistinguishable homogeneous agents: A convex optimization approach

The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this paper, the discrete-time, finite-horizon case is considered, where the agents are also assumed to be homogeneous and indistinguishable. The latter means that the agents all have the same dynamics and objective functions and the observations are in terms of “snap shots” of all agents at different time instants, but what is not known is “which agent moved where” for consecutive observations. This absence of linked optimal trajectories makes the problem challenging. We first show that this problem is globally identifiable. Then, for the case of noiseless observations, we show that the true cost matrix, and hence the closed-loop system matrices, can be recovered as the unique global optimal solution to a convex optimization problem. Next, for the case of noisy observations, we formulate an estimator as the unique global optimal solution to a modified convex optimization problem. Moreover, the statistical consistency of this estimator is shown. Finally, the performance of the proposed method is demonstrated by a number of numerical examples.

Direction of Arrival Estimation and Phase-Correction for Noncoherent Subarrays: A Convex Optimization Approach

Estimating the direction of arrival (DOA) of sources is an important problem in aerospace and vehicular communication, localization, and radar. In this article, we consider a challenging multisource DOA estimation task, where the receiving antenna array is composed of noncoherent subarrays, i.e., subarrays that observe different unknown phase shifts at every snapshot (e.g., due to waiving the demanding synchronization of local oscillators across the entire array). We formulate this problem as the reconstruction of joint sparse and low-rank matrices and solve the problem’s convex relaxation. To scale the optimization complexity with the number of snapshots better than general-purpose solvers, we design an optimization scheme, based on integrating the alternating direction method of multipliers and the accelerated proximal gradient techniques, which exploits the structure of the problem. While the DOAs can be estimated from the solution of the aforementioned convex problem, we further show how an improvement is obtained if, instead, one estimates from this solution only the subarrays’ phase shifts. This is done using another, computationally light, convex relaxation that is practically tight. Using the estimated phase shifts, “phase-corrected” observations are created and a final plain (“coherent”) DOA estimation method can be applied. Numerical experiments show the performance advantages of the proposed strategies over existing methods.

Primal–dual interior-point algorithm for electricity cost minimization in a prosumer-based smart grid environment: A convex optimization approach

This study proposes a primal–dual interior-point algorithm, which is used by the prosumers to efficiently manage the operation of their generating and consuming devices, to maximize their own profits while contributing to the stability of the overall electricity grid. The energy management problem investigated in this study is formulated as a convex optimization problem and the primal–dual interior-point algorithm is leveraged to acquire the optimal solution which minimizes the energy cost for prosumers in a smart grid environment. The proposed algorithm considers the cost of energy generation by each available device or the charge of a utility company, as well as the predicted consumption and production levels of the facility, and develops an operating plan that maximizes the prosumer’s profitability. The cost function for energy generation is convex, as are the constraints that must be satisfied. The primal–dual interior-point algorithm is an efficient algorithm and has attracted attention in the optimization community. The proposed algorithm is evaluated on three prosumer profiles that have different generation and storage characteristics. A variable pricing structure for power supplied or bought by the utility company is considered in this study and a scenario in which prosumers are not allowed to sell to the utility company. It is evident from the simulation results of the MATLAB environment that scenario 1 generates the minimum cost operation profiles compared to scenario 2. The effectiveness and the robustness of the proposed algorithm are demonstrated in the optimal solution obtained in solving the energy management problem.

Bilevel aggregator-prosumers' optimization problem in real-time: A convex optimization approach

This paper proposes a Real-Time Market (RTM) platform for an aggregator and its corresponding prosumers to participate in the electricity wholesale market. The proposed energy market platform is modeled as a bilevel optimization problem where the aggregator and the prosumers are considered as self-interested agents. We present a convex optimization problem which can capture a subset of the set of global optima of the bilevel problem as its optimal solution.

Encoding–decoding-based secure filtering for neural networks under mixed attacks

This paper is concerned with the set-membership filtering issue for a class of artificial neural networks subject to mixed attacks. The encoding–decoding communication mechanism is adopted in the processing of data sharing between neurons. During the information exchanges among neurons, both injection and DoS attacks are concurrently considered to reflect the practical operating conditions of the investigated neural networks. The purpose of the addressed problem is to present an algorithm to estimate the neurons’ states in the presence of mixed attacks, while guaranteeing the estimation errors at each neuron are confined within certain prescribed ellipsoidal region. Sufficient conditions are derived, in terms of convex optimization approach, to ensure the existence of desired filter, and the explicit filtering parameters are obtained via solving the provided set of matrix inequalities. Finally, a numerical simulation example is proposed to show the validity of the obtained theoretical results.

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

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 require 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 computed.

Largest small polygons: a sequential convex optimization approach

A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n=2m$ vertices is not known when $m\ge 7$. Finding the largest small $n$-gon for a given number $n\ge 3$ can be formulated as a nonconvex quadratically constrained quadratic optimization problem. We propose to solve this problem with a sequential convex optimization approach, which is an ascent algorithm guaranteeing convergence to a locally optimal solution. Numerical experiments on polygons with up to $n=128$ sides suggest that the optimal solutions obtained are near-global. Indeed, for even $6 \le n \le 12$, the algorithm proposed in this work converges to known global optimal solutions found in the literature.

Electrodermal Activity for Measuring Cognitive and Emotional Stress Level.

Stress can lead to harmful conditions in the body, such as anxiety disorders and depression. One of the promising noninvasive methods, which has been widely used in detecting stress and emotion, is electrodermal activity (EDA). EDA has a tonic and phasic component called skin conductance level and skin conductance response (SCR). However, the components of the EDA cannot be directly extracted and need to be deconvolved to obtain it. The EDA signals were collected from 18 healthy subjects that underwent three sessions – Stroop test with increasing stress levels. The EDA signals were then deconvoluted by using continuous deconvolution analysis (CDA) and convex optimization approach to electrodermal activity (cvxEDA). Four features from the result of the deconvolution process were collected, namely sample average, standard deviation, first absolute difference, and normalized first absolute difference. Those features were used as the input of the classification process using the extreme learning machine (ELM). The output of classification was the stress level; mild, moderate, and severe. The visual of the phasic component using cvxEDA is more precise or smoother than the CDA's result. However, both methods could separate SCR from the original skin conductivity raw and indicate the small peaks from the SCR. The classification process results showed that both CDA and cvxEDA methods with 50 hidden layers in ELM had a high accuracy in classifying the stress level, which was 95.56% and 94.45%, respectively. This study developed a stress level classification method using ELM and the statistical features of SCR. The result showed that EDA could classify the stress level with over 94% accuracy. This system could help people monitor their mental health during overworking, leading to anxiety and depression because of untreated stress.

Dynamic Anomaly Detection With High-Fidelity Simulators: A Convex Optimization Approach

The main objective of this article is to develop scalable dynamic anomaly detectors with high-fidelity simulators of power systems. On the one hand, models in high-fidelity simulators are typically “intractable” if one opts to describe them in a mathematical formulation in order to apply existing model-based approaches from the anomaly detection literature. On the other hand, pure data-driven methods developed primarily in the machine learning literature neglect our knowledge about the underlying dynamics of power systems. In this study, we combine tools from these two mainstream approaches to develop a data-assisted model-based diagnosis filter utilizing both the knowledge from a picked abstract model and also the data of simulation results from high-fidelity simulators. The proposed diagnosis filter aims to achieve two desired features: (i) performance robustness with respect to model mismatch; (ii) high scalability. To this end, we propose a tractable (convex) optimization-based reformulation in which decisions are the filter parameters, the model-based information introduces feasible sets, and the data from the simulator forms the objective function to-be-minimized regarding the effect of model mismatch on the filter performance. To validate the theoretical results, we implement the developed diagnosis filter in DIgSILENT PowerFactory to detect false data injection attacks on the Automatic Generation Control measurements in the three-area IEEE 39-bus system.

A convex optimization approach to synthesizing state feedback data-driven controllers for switched linear systems

This paper seeks to develop a computationally tractable framework for data-driven control of switched linear systems. Specifically, given a model structure and experimental data collected at different operating points, we seek to directly design a state-feedback controller that stabilizes a system that arbitrarily switches amongst all sub-systems that could have generated the observed data, without an explicit plant identification step. The main result of the paper shows that this robust optimization problem can be recast, through the use of duality, into a polynomial optimization form and efficiently solved, leading to a robust controller with guaranteed ℓ∞ worst-case performance. The effectiveness of the proposed technique is illustrated with several examples, including control of the horizontal motion of a quadcopter

A robust convex optimization approach to design a hierarchical organ transplant network: A case study

Organ transplant network as one of the most complex and challenging networks among healthcare systems, requires an effective supply chain design. In this research, a novel bi-objective hierarchical location-allocation model is developed to design an organ transplant network. The goal is to simultaneously minimize the total time and costs, and maximize the geographic parity in the network under supply and demand uncertainty. Different transportation modes are considered in the developed network, and the optimum transportation mode is selected after solving the model. The augmented ε-constraint technique is applied to solve the multi-objective model. Furthermore, a convex robust optimization approach is developed to tackle uncertain nature of the parameters. Finally, a case study is presented and the optimal solutions of the developed models are calculated and analyzed.

Deep learning driven physical layer security for a simultaneously wireless information and power transfer network

Artificial intelligent approaches have been considered as the promising techniques to enable smart communications in future wireless networks. In this paper, we investigate the deep learning based resource allocation approach for secure transmission in a simultaneously wireless information and power transfer (SWIPT) network. In particular, we design the resource allocations to maximize the minimum achievable secrecy rate of the legitimate user under the constraints of energy harvesting requirements of the energy receivers (ERs). Conventionally, the optimal or suboptimal solutions of resource allocation problems can be obtained by exploiting convex optimization approaches, which are often developed based on iterative algorithms, and always result in long computational time. To satisfy ultra low latency demands and achieve physical layer security for future SWIPT systems, we develop a DNN based approach that has the capability to optimize the power allocations for a SWIPT network, where the computational time and complexity have been significantly cut down. Numerical results are provided to illustrate that the effectiveness of our proposed DNN based approach, which is capable to achieve near optimal secrecy rate performances in comparing with convex optimization approach.

Joint Power and Gain Allocation in MDM-WDM Optical Communication Networks Based on Enhanced Gaussian Noise Model

Achieving reliable communication over different wavelength channels and modes is one of the main goals of Mode Division Multiplexing-Wavelength Division Multiplexing (MDM-WDM) transmission. The reliability can be described by the minimum Signal to Noise Ratio (SNR) margin which depends on launch power, the gain of Few-Mode Erbium-Doped Fiber Amplifiers (FM-EDFA), and the nonlinear impairments of Few-Mode Fiber (FMF). In this paper, we develop the Enhanced Gaussian Noise (EGN) nonlinear model for FMF, which can be used in both weak and strong coupling regimes. We validate the model by comparing simulation results with those obtained through the Split-Step Fourier Method. Based on our proposed EGN model, we address the problem of joint optimized power and gain allocation based on minimum SNR margin maximization when accounting for practical FM-EDFA constraints such as saturation power and maximum gain. The problem is solved using a convex optimization approach and considering different scenarios such as the best equal power, optimized power, and joint optimized power and gain. Results demonstrate that the minimum SNR margin improvement for the joint optimized power and gain allocation compared to the best equal power allocation is <inline-formula> <tex-math notation="LaTeX">$1.4~dB$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$1.7~dB$ </tex-math></inline-formula> for MDM-single channel and single-mode fiber-WDM systems, respectively.