Quadratically Constrained Quadratic Programming Research Articles

Convex Quadratic Programming for Computing Geodesic Distances on Triangle Meshes

Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring that the norm of the triangle-wise estimated gradients is not larger than 1 is preferable compared to the widely used eikonal condition. Inspired by this, we formulate the geodesic distance field problem as a Quadratically Constrained Linear Programming (QCLP) problem. This formulation can be further adapted into a Quadratically Constrained Quadratic Programming (QCQP) problem by incorporating considerations for smoothness requirements. Specifically, when enforcing a Hessian-energy-based smoothing term, our formulation, named QCQP-Hessian, effectively mitigates the cusps in the geodesic isolines within the near-ridge area while maintaining accuracy in the off-ridge area. We conducted extensive experiments to demonstrate the accuracy and smoothness advantages of QCQP-Hessian.

On semidefinite descriptions for convex hulls of quadratic programs

Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP) relaxation. In this paper we study when the convex hull of the epigraph of a QCQP coincides with the projected epigraph of the SDP relaxation. We present a sufficient condition for convex hull exactness and show that this condition is further necessary under an additional geometric assumption. The sufficient condition is based on geometric properties of Γ, the cone of convex Lagrange multipliers, and its relatives Γ1 and Γ∘.

Collision-free automatic berthing of maritime autonomous surface ships via safety-certified active disturbance rejection control

This paper addresses the automatic berthing of a maritime autonomous surface ship operating in a confined water environment subject to static obstacles, dynamic obstacles, thruster constraints, and space constraints due to shorelines. A safety-certified active disturbance rejection control (ADRC) method is proposed for achieving the automatic berthing task of an MASS in the presence of model uncertainties and ocean disturbances. An extended state observer (ESO) based on a second-order robust exact differentiator (RED) is employed to estimate an extended state vector consisting of internal model uncertainties and external ocean disturbances. With the aid of the RED-based ESO, a nominal ADRC law is designed to achieve the position and heading stabilization. To avoid collisions with static obstacles, dynamic obstacles, and shorelines, input-to-state safe high-order control barrier functions are used to guarantee safety. Optimized control signals are obtained based on a constrained quadratic programming (QP) problem within safety constraints. In order to translate the control signals into the individual thruster command, a constrained QP problem is further used to search for optimized commands in real time. It is proven that the closed-loop automatic berthing system is input-to-state stable. By using the proposed method, the MASS is able to reach the desired position and heading with collision avoidance. Simulation results verify the effectiveness of the proposed safety-certified ADRC method for automatic berthing.

Cryo-forum: A framework for orientation recovery with uncertainty measure with the application in cryo-EM image analysis

In single-particle cryo-electron microscopy (cryo-EM), efficient determination of orientation parameters for particle images poses a significant challenge yet is crucial for reconstructing 3D structures. This task is complicated by the high noise levels in the datasets, which often include outliers, necessitating several time-consuming 2D clean-up processes. Recently, solutions based on deep learning have emerged, offering a more streamlined approach to the traditionally laborious task of orientation estimation. These solutions employ amortized inference, eliminating the need to estimate parameters individually for each image. However, these methods frequently overlook the presence of outliers and may not adequately concentrate on the components used within the network. This paper introduces a novel approach that uses a 10-dimensional feature vector to represent the orientation and applies a Quadratically-Constrained Quadratic Program to derive the predicted orientation as a unit quaternion, supplemented by an uncertainty metric. Furthermore, we propose a unique loss function that considers the pairwise distances between orientations, thereby enhancing the accuracy of our method. Finally, we also comprehensively evaluate the design choices in constructing the encoder network, a topic that has not received sufficient attention in the literature. Our numerical analysis demonstrates that our methodology effectively recovers orientations from 2D cryo-EM images in an end-to-end manner. Notably, the inclusion of uncertainty quantification allows for direct clean-up of the dataset at the 3D level. Lastly, we package our proposed methods into a user-friendly software suite named cryo-forum, designed for easy access by developers.

Energy storage system coordinated with phase-shifting transformer and dynamic rating equipment for optimal operation of wind-rich smart power networks

Emergence of flexibility devices into smart power systems can assist the power system operators in making effective and economical decisions for the power system scheduling. These devices include energy storage system (ESS), phase-shifting transformer (PST), dynamic transformer rating (DTR), and dynamic line rating (DLR). In this paper, an approach is proposed for optimal day-ahead scheduling of power system using coordinated operation of ESS, PST, DTR, and DLR units under high wind power penetration situation. The aim is to minimize operational, load shedding, and wind power curtailment costs by regarding all the problem constraints. All of the model's relations as well as AC power flow equations have been convexified in order to construct a mixed-integer quadratically-constrained programming (MIQCP) model whose solution will obtain global optimum results. The developed model is implemented in GAMS and applied to the IEEE 24-bus system under various case studies, and the obtained results are investigated thoroughly. By coordinated operation of the employed flexibility devices, the loading of transformers and lines reach 159 % and 246 % compared to their nominal rating without violation of temperature limitations. Through releasing the capacity of lines and transformers, the total scheduling cost is reduced by about 52 % compared to traditional operation. Also, the whole energy of wind farms is utilized without any curtailment or constraints violation.

Globally Optimal Inverse Kinematics as a Non-Convex Quadratically Constrained Quadratic Program

Globally Optimal Inverse Kinematics as a Non-Convex Quadratically Constrained Quadratic Program

Optimal design of hydrogen-based storage with a hybrid renewable energy system considering economic and environmental uncertainties

Hydrogen and electricity derived from renewable sources present feasible alternative energy options for the decarbonisation of the transportation and power sectors. This study presents the utilisation of hydrogen generated from solar and wind energy resources as a clean fuel for mobility and backup storage for stationary applications under economic and environmental uncertainties. This is achieved by developing a detailed techno-economic model of an integrated system consisting of a hydrogen refuelling station and an electric power generation system using Mixed Integer Quadratic Constrained Programming (MIQCP), which is further relaxed to Mixed Integer Linear Programming (MILP). The model is implemented in the Advanced Interactive Multidimensional Modelling Software (AIMMS) and considering the inherent uncertainties in the wind resource, solar resource, costs and discount rate, the total cost of the three configurations (Hybrid PV-Wind, Standalone PV, and Standalone wind energy system) was minimised using robust optimisation technique, and the corresponding optimal sizes of the components, levelised cost of energy (LCOE), excess energy, greenhouse emission avoided, and carbon tax were evaluated. The levelised cost of the deterministic optimisation solution for all the configuration ranges between 0.0702 $/kWh to 0.0786 $/kWh, while the levelised cost of the robust optimisation solution ranges between 0.07188 $/kWh to 0.1125 $/kWh. The proposed integration has the advantages of affordable hydrogen and electricity prices, minimisation of carbon emissions and grid export of excess energy.

A Communication Anti-Jamming Scheme Assisted by RIS with Angular Response.

By optimizing the reconfigurable intelligent surface (RIS) reflection coefficients, the channel capacity of legitimate users can be increased, thereby enhancing the anti-jamming performance of communication systems. However, existing studies on RIS-assisted anti-jamming assume that there is no coupling between the RIS reflection coefficients and the incident angle of electromagnetic (EM) waves, which is quite unreasonable. Therefore, we consider the effect of the incident angle of EM waves on the reflection coefficients of the RIS and propose a communication anti-jamming scheme assisted by an RIS with angular response. Specifically, a problem is formulated to optimize the RIS reflection coefficients so that the legitimate signal is amplified, but the jamming signal is attenuated, thus enhancing the legitimate channel capacity. However, the coupling of the EM incident angle and the RIS reflection coefficients causes the problem to be non-convex. To tackle this problem, we equivalently transform the RIS reflection coefficients optimization problem into a quadratically constrained quadratic programming (QCQP) problem using the complex Taylor expansion and the multidimensional complex quadratic transform (MCQT) and solve it utilizing the alternating direction method of the multipliers (ADMM) algorithm. The simulation results reveal that, compared to other schemes supported by RIS without angular response, the proposed scheme is able to achieve a significant improvement in the anti-jamming performance.

Reactive mobile manipulation based on dynamic dual-trajectory tracking

The letter presents an online obstacle avoidance strategy for a nonholonomic mobile manipulator, including dual-trajectory generation for the mobile base(MB) and end effector(EE), as well as whole-body reactive obstacle avoidance. The feasible region of the manipulator’s workspace is generated by traversing the path of the MB, and the spatio-temporal trajectory of the EE is generated by quadratically constrained quadratic programming(QCQP) planning, satisfying the physical constraints and obstacle avoidance constraints. The reactive obstacle avoidance strategy is based on quadratic programming(QP), using singularity avoidance and EE trajectory tracking tasks as soft constraints with different priorities. Considering the nonholonomic constraints and motion differences of MB, we employ a dynamic tracking approach to avoid obstacles of MB. Additionally, an adaptive weight method is utilized to adjust the priority of MB path tracking task, effectively preventing joint velocity jitter during the insertion process. Our strategy has been proven to generate obstacle avoidance trajectories for EE in real-time and ensure safe joint velocities for MB and the manipulator through simulation and real-world scenarios.

Robust Adaptive Beamforming for Interference Suppression Based on SNR

Robust adaptive beamforming (RAB) can be used to suppress interference signals while retaining the desired signals received by a sensor array. However, desired signal self-cancellation and model mismatch can affect RAB performance. In this paper, a novel interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for RAB to solve these problems. The proposed method divides the desired signal into two ranges according to the input signal-to-noise ratio (SNR), namely low SNR and high SNR. In the low SNR range, INCM reconstruction directly uses the same sample covariance matrix as the sample matrix inversion (SMI) beamformer to retain the advantages of the traditional SMI algorithm. In the high SNR range, the eigenvalues of the sample covariance matrix are used to estimate the interference power and noise power. The optimized interference steering vector (SV) is obtained by solving a quadratic convex optimization problem in an interference subspace. The INCM is reconstructed from the interference SVs, interference power, and noise power. The reconstructed INCM is then used to correct the desired signal SV via maximizing the beamformer output power. This is achieved by solving a quadratically constrained quadratic programming (QCQP) problem. Analysis and simulation results are presented which demonstrate that the proposed method performs well under a variety of mismatch conditions.

Enhanced range-doppler algorithm for SAR image formation

A Synthetic Aperture Radar (SAR) system is a powerful source of information due to its capability to operate day and night and in all weather conditions. It is essential for military and civilian purposes. Pulse-focusing is employed by the SAR system for achieving both long-range detection and fine-range resolution. The Range-Doppler Algorithm (RDA) is the most popular pulse-focusing technique for creating images from coherent SAR data. Pulse compression techniques for SAR signal processing targets seek to improve map resolution, lower peak power, and increase the Signal-to-Noise Ratio (SNR) of the detected object. This paper demonstrates an enhanced RDA algorithm that uses a modified pulse compression technique based on mismatched filter optimization where Quadratic Constrained Quadratic Program (QCQP) is used. The performance evaluation of the proposed method is performed using visual assessment and the standard image quality metrics peak-side-lobe-ratio (PSLR), impulse-response-width (IRW), and integrated-side-lobe-ratio (ISLR). Simulated and real SAR raw data are used for performance evaluation. The experimental results demonstrate the proposed method’s robustness, efficiency, and reliability in providing a higher-quality SAR image than the traditional RDA algorithm.

Effect of climate on the optimal sizing and operation of seasonal ice storage systems

Seasonal thermal storage systems can reduce the temporal mismatch between renewable energy availability and energy demand. Ice storage systems exhibit a non-linear behaviour in the heat exchange and storage processes, complicating the formulation of optimal design and operation problems. In this work, we propose a mixed-integer quadratically-constrained programming formulation, which minimizes the Levelized Cost of Energy for space heating and cooling, including sizing of a supporting PV array. The optimization was repeated for different storage volumes, finding the system optimal operation in each case –and thereby the optimal system sizing. The heating and cooling demands were computed from an archetypal office building, placed in three reference locations with cold and semi-arid, warm and humid continental, and temperate and humid continental climates. Results show that the optimal PV size decreases with growing ice storage volume, and an ice storage works best in a temperate continental climate, covering up to 47% of the cooling demand with a 250 m 3 storage.

Virtual covariance matrix reconstruction-based adaptive beamforming for small aperture array.

Recently, many robust adaptive beamforming (RAB) algorithms have been proposed to improve beamforming performance when model mismatches occur. For a uniform linear array, a larger aperture array can obtain higher array gain for beamforming when the inter-sensor spacing is fixed. However, only the small aperture array can be used in the equipment limited by platform installation space, significantly weakening beamforming output performance. This paper proposes two beamforming methods for improving beamforming output in small aperture sensor arrays. The first method employs an integration algorithm that combines angular sector and gradient vector search to reconstruct the interference covariance matrix (ICM). Then, the interference-plus-noise covariance matrix (INCM) is reconstructed combined with the estimated noise power. The INCM and ICM are used to optimize the desired signal steering vector (SV) by solving a quadratically constrained quadratic programming (QCQP) problem. The second method proposes a beamforming algorithm based on a virtual extended array to increase the degree of freedom of the beamformer. First, the virtual conjugated array element is designed based on the structural characteristics of a uniform linear array, and received data at the virtual array element are obtained using a linear prediction method. Then, the extended INCM is reconstructed, and the desired signal SV is optimized using an algorithm similar to the actual array. The simulation results demonstrate the effectiveness of the proposed methods under different conditions.

Risk-based distributionally robust optimal dispatch for multiple cascading failures in regional integrated energy system using surrogate modeling

Regional integrated energy system (RIES) with the close coupling of multiple energies faces various cascading failure risks in its operation, and formulating the risk-based optimal dispatch scheme is important to ensure the secure and economic operation of the RIES. Considering that the occurrence probability of each subsequent failure path caused by the initial failure in the cascading failure chain varies with the change of dispatch scheme, the cooling/heating and gas pipeline dynamics and the uncertainty of renewable energy, a risk-based distributionally robust optimal dispatch model for multiple cascading failures in a RIES is proposed. A kernel ambiguity set is constructed by using the maximum mean discrepancy between the real and reference probability distributions and the kernel mean embedding technology, which can obtain the more accurate worst-case probability distribution. Moreover, a surrogate modeling method based on piecewise convex quadratic functions is proposed to learn the mapping between the cascading failure risks and the decision variables, and the original large-scale mixed integer nonlinear programming model is transformed into a small-scale mixed integer quadratic constrained programming model for efficient solution. Finally, case study on an actual RIES demonstrates the effectiveness and advantages of the proposed method. Compared to optimal dispatch without considering the cascading failure risks, the proposed method can reduce the total failure risk cost by nearly 60%.

Techno-economic investigation of hybrid peaker plant and hydrogen refuelling station

The power and transport sectors are responsible for significant emissions of greenhouse gases. Therefore, it is imperative that substantial efforts are directed towards the decarbonisation of these industries. This study establishes a combined-solar-wind system's economic and technical practicality for producing hydrogen for an onsite hydrogen refuelling station (HRS) and electricity to meet peak demand. To minimise the levelised cost of electricity and maximise the system's reliability at different commercial locations in South Africa, the dual-objective optimisation sizing is carried out using Mixed Integer Quadratic Constrained Programming (MICQP) model and was executed with an Advanced Multi-dimensional Modelling System (AIMMS) [61], [62]. The levelised costs of electricity and hydrogen at Johannesburg, Pretoria and Cape Town for 2 MW grid export benchmark are 74.2 $/MWh/5.85 $/kg, 76.3 $/MWh/5.97 $/kg and 50 $/MWh/4.45 $/kg respectively. The CO₂ equivalent emissions (tonnes) are 54,000, 55,800, 59,000 and the corresponding carbon taxes ($) avoided for the locations are 432,100, 446,200, and 472,000 for Johannesburg, Pretoria and Cape Town respectively. The results of the framework show that it can be adopted as a viable and fossil-free replacement for conventional peaking generators.

Energy-Efficient Joint Collaborative and Passive Beamforming for Intelligent-Reflecting-Surface-Assisted Wireless Sensor Networks

Intelligent reflecting surface (IRS) provides a promising technology that can improve the energy efficiency of wireless communications, by building the controllable wireless propagation environment with the utilization of massive passive reflecting elements. Motivated by this, we apply the IRS to assist the data collection based on collaborative beamforming in Wireless Sensor Networks (WSNs). With the objective to maximize the network lifetime, we present an energy efficient joint collaborative and passive beamforming design for an IRS-assisted WSN, which jointly optimizes the beamforming vector for all nodes and phase shifts for IRS’s reflecting elements. To efficiently resolve the joint optimization problem, we develop a penalty dual decomposition (PDD) based algorithm combined with augmented Lagrangian method, penalty-based method and block coordinate descent algorithm, which decomposes the joint optimization problem into four simplified subproblems. Especially in solving IRS’s phase shifts optimization subproblem, we formulate this subproblem as a quadratically constrained quadratic programming (QCQP) problem and further propose a low computational complexity approximate iteration algorithm to resolve this QCQP problem, which iteratively linearizes this QCQP problem to a sequence of approximate programming with linear equality constraints, whose closed-form solution is presented. Theoretical analysis indicates the proposed algorithm can converge to a KKT solution. Simulation results indicate that the IRS-assisted design and proposed algorithm improve the energy efficiency and prolong the network lifetime as compared to alternative algorithms.

Modulus Constrained Minimax Radar Code Design Against Target Interpulse Fluctuation

In the presence of colored Gaussian disturbance, this paper considers the robust transmit code and receiver filter design against target interpulse fluctuation while guaranteeing the dynamic range and energy of the transmit code. Aiming at enhancing the worst-case Signal-to-Noise-Ratio (SNR) over a spherical set, the design is cast as a non-convex minimax problem. It is shown that the filter can be directly derived based on the strong max-min property of the objective function. Then, the semi-definite relaxation form of the resultant problem is proved to be hidden convex by exploiting the strong duality of the Quadratically-Constrained Quadratic Programming (QCQP) problem. Finally, the robust code-filter pair can be effectively synthesized based on a randomization scheme. At the analysis stage, numerical results are shown to highlight the superiority of the proposed design.

Distributed conditional cooperation model predictive control of interconnected microgrids

In this paper, we propose a model predictive control based operation strategy that allows for power exchange between interconnected microgrids. Particularly, the approach ensures that each microgrid benefits from power exchange with others. This is realised by including a condition which is based on the islanded operation cost. The overall model predictive control problem is posed as a mixed-integer quadratically-constrained program and solved using a distributed algorithm that iteratively updates continuous and integer variables. For this algorithm, termination, feasibility and computational properties are discussed. The performance and the computational benefits of the proposed strategy are highlighted in an illustrative case study.

Integrated sensing and communication waveform design in the Internet of Vehicles

We design an integrated sensing and communication (ISAC) transmission waveform with total transmission power, waveform similarity, and peak-to-average power ratio (PAPR) constraints in the Internet of Vehicles (IoV). The integrated waveform can complete radar target detection while communicating with downlink cellular users. The design of IoV with ISAC can not only improve the spectrum efficiency, but also further promote the integration of communication and sensing equipment. In this paper, the IoV with ISAC is formally modeled from the communication view and sensing view respectively. On this basis, taking the joint optimization of multi-user interference (MUI) total energy and Cramér Rao Bound (CRB) as the objective function, the transmission waveforms are designed with total transmission power, waveform similarity, and PAPR constraints respectively. To obtain the global optimal solution, we adopt a low complexity algorithm to solve the optimization problem under the total transmit power constraint and the optimization problem based on waveform similarity and PAPR constraints is further transformed into a nonconvex quadratically constrained quadratic programming (QCQP) problem, which is solved by using the semidefinite relaxation (SDR) technique. By ranking one approximation of the constrained optimization problem, it can be transformed into the solution of semidefinite programming (SDP) problems. The numerical results show that the designed ISAC transmission waveform can achieve an efficient tradeoff between sensing and communication performance, and each KPI is superior to one of the only communication and only sensing waveform design schemes. And it can improve the real-time information interaction ability of the IoV.

Flexible and sustainable scheduling of electric power grids: A dynamic line and transformer rating based approach under uncertainty condition

Integration of renewable and sustainable energies into the electric power grids has affected planning and operation problems of the power system. Voltage and congestion as well as uncertainty issues are some challenges regarding this integration. Dynamic line and transformer ratings, known as DLR and DTR, are kinds of smart-grid technologies that can help alleviation of above-mentioned problems and perform a flexible scheduling for the power system. In this paper, the DLR and DTR have been simultaneously incorporated in optimal power flow (OPF) problem in wind-energy-integrated power systems considering the presence of uncertainties. The aim is to perform an optimal day-ahead scheduling of thermal and wind power units where the uncertainty of DLR and DTR as well as that of wind power generation are considered. The uncertainty scenarios are generated by Monte-Carlo method where k-means clustering algorithm is employed to reduce the number of scenarios within a scenario-based stochastic optimization. As the AC power flow and dynamic rating relations have non-convex nature, they have been convexified in order to formulate the optimization problem as a mixed-integer quadratically-constrained programming (MIQCP). The proposed approach is applied to IEEE-24-bus system in different experiments in GAMS environment. The simulations demonstrate efficiency of the conducted approach in reducing operating costs, minimizing load shedding cost, and maximum scheduling of wind power units as sustainable and clean energy resources.