Quadratically Constrained Quadratic Programming Research Articles

Techno-economic optimization and feasibility of PCM-based seasonal thermal energy storage systems for district heating and cooling

Phase change materials (PCM) are an attractive seasonal thermal energy storage solution for load shifting due to relatively high energy density. Nevertheless, the choice of the right design parameters, such as storage size and phase-change temperature, is nontrivial, as these are tightly linked to the expected seasonal operation of the storage. This paper presents a combined design and operation optimization framework for sizing PCM-based seasonal thermal storage, which can capture dynamic behaviour of the storage in sensible and latent phases, and its impact on the efficiency of connected heat pumps and chillers. The proposed method, formulated as a mixed integer quadratically-constrained programming problem, was applied to a case study of heating-dominated district. It was found that the optimal PCM melting temperature equals to the heating demand supply temperature, thus removing the need of a heat pump to discharge the storage. The optimal operation of storage requires a full charging and discharging cycle of both latent and liquid phase. Higher CO2 emission price does not lead to a significant reduction of CO2 emissions, but the storage size does, leading to a higher heating coverage ratio of the storage, and consequently CO2 emissions and cost savings, which can be further enhanced with PV integration. The economic analysis indicates that, unless other benefits such as storage volume reduction are accounted for, PCM cost should drop by a factor 4 to make this solution economically viable for seasonal storage.

Certifiably optimal rotation and pose estimation based on the Cayley map

We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem setups that assume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevin distribution or chordal distance) for isotropic rotational uncertainty. However, another common way to represent uncertainty for rotations and poses is to define anisotropic noise in the associated Lie algebra. Starting from a noise model based on the Cayley map, we define our estimation problems, convert them to Quadratically Constrained Quadratic Programs (QCQPs), then relax them to Semidefinite Programs (SDPs), which can be solved using standard interior-point optimization methods; global optimality follows from Lagrangian strong duality. We first show how to carry out basic rotation and pose averaging. We then turn to the more complex problem of trajectory estimation, which involves many pose variables with both individual and inter-pose measurements (or motion priors). Our contribution is to formulate SDP relaxations for all these problems based on the Cayley map (including the identification of redundant constraints) and to show them working in practical settings. We hope our results can add to the catalogue of useful estimation problems whose solutions can be a posteriori guaranteed to be globally optimal.

Global optimization for large‐scale water network synthesis based on dynamic partition and adaptive bound tightening

AbstractThe synthesis of large‐scale integrated water networks is typically formulated as nonconvex mixed‐integer quadratic constrained programming (MIQCP) or QCP problems. With the complexity arising from bilinear terms in modeling mass flows of contaminants and binary variables representing the presence of units or streams, numerous local optima exist, thus presenting a significant optimization challenge. This study introduces a deterministic global optimization algorithm based on mixed‐integer programming (MIP) to tackle such problems. The approach involves dynamically strengthening the relaxed problems to converge towards the original problems. A simultaneous partition strategy is proposed combining locally uniform division with dynamic partitioned variables choosing. Furthermore, several adaptive bound contraction schemes are introduced to efficiently manage the size of the relaxed problems, assisting in accelerating the solution process. The algorithm's effectiveness and robustness are demonstrated with a large test set, showing superior performance compared to commercial solvers specifically on MIQCP problems.

Robust adaptive beamforming for cylindrical uniform conformal arrays based on low-rank covariance matrix reconstruction

Recently, conformal arrays have attracted considerable interest because such arrays can provide reduced radar cross-section and increased angle coverage. In this article, we devise a robust adaptive beamforming (RAB) approach using cylindrical uniform conformal array (CUCA). Firstly, we derive the minimum variance distortionless response (MVDR) beamformer for the CUCA by utilizing the noise subspace of interference covariance matrix (ICM) and steering vector (SV) of the signal-of-interest (SOI). Subsequently, the ICM is reconstructed by estimating the noise-free covariance matrix of the CUCA outputs and the interference projection matrix. Specifically, the noise-free covariance matrix can be regarded as multiple low-rank covariance matrices, and each low-rank matrix is reconstructed by formulating a nuclear norm minimization (NNM) problem. With the reconstructed covariance matrix, the 2-D DOAs of sources are determined by employing 2-D MUSIC spectrum to form the interference projection matrix. In addition, the SOI SV is estimated by solving a quadratically constrained quadratic programming (QCQP) problem. Numerical results demonstrate that the proposed approach is obviously superior to the existing RAB techniques.

Impossible Boomerang Attacks Revisited

The impossible boomerang (IB) attack was first introduced by Lu in his doctoral thesis and subsequently published at DCC in 2011. The IB attack is a variant of the impossible differential (ID) attack by incorporating the idea of the boomerang attack. In this paper, we revisit the IB attack, and introduce the incompatibility of two characteristics in boomerang to the construction of an IB distinguisher. With our methodology, all the constructions of IB distinguisher are represented in a unified manner. Moreover, we show that the related-(twea)key IB distinguishers possess more freedom than the ones of ID so that it can cover more rounds.We also propose a new tool based on Mixed-Integer Quadratically-Constrained Programming (MIQCP) to search for IB attacks. To illustrate the power of the IB attack, we mount attacks against three tweakable block ciphers: Deoxys-BC, Joltik-BC and SKINNY. For Deoxys-BC, we propose a related-tweakey IB attack on 14-round Deoxys-BC-384, which improves the best previous related-tweakey ID attack by 2 rounds, and we improve the data complexity of the best previous related-tweakey ID attack on 10-round Deoxys-BC-256. For Joltik-BC, we propose the best attacks against 10-round Joltik-BC-128 and 14-round Joltik-BC-192 with related-tweakey B attack. For SKINNY-n-3n, we propose a 27-round related-tweakey IB attack, which improves both the time and the memory complexities of the best previous ID attack. We also propose the first related-tweakey IB attack on 28-round SKINNY-n-3n, which improves the previous best ID attack by one round.

Model predictive control of wakes for wind farm power tracking

In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows the tracking of a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows the estimation of the rotor effective wind speeds at downstream turbines, based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.

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

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

A hybrid algorithm for quadratically constrained quadratic optimization problems

Quadratically Constrained Quadratic Programs (QCQPs) are an important class of optimization problems with diverse real-world applications. In this work, we propose a variational quantum algorithm for general QCQPs. By encoding the variables in the amplitude of a quantum state, the requirement for the qubit number scales logarithmically with the dimension of the variables, which makes our algorithm suitable for current quantum devices. Using the primal-dual interior-point method in classical optimization, we can deal with general quadratic constraints. Our numerical experiments on typical QCQP problems, including Max-Cut and optimal power flow problems, demonstrate better performance of our hybrid algorithm over classical counterparts.

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.

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.

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∘.

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.

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.