Non-convex Optimization Model Research Articles

Collaborative Optimization for Active Distribution Network with Soft Open Point and Energy Storage

Background: The increasing use of high-penetration distributed clean energy has led to voltage fluctuations in the distribution network that surpass safety limits and pose challenges to economic and low-carbon operation. Traditional voltage regulation devices are unable to meet the real-time high-precision voltage control needs when encountering frequent fluctuations due to physical limitations. The Soft Open Point (SOP) can provide continuous reactive power to achieve rapid voltage regulation. Objective: We propose a collaborative optimization approach that fully considers the regulatory capabilities of SOP and energy storage to eliminate voltage violations and reduce network losses. Methods: This study introduces an active distribution network reactive power voltage optimization approach that incorporates intelligent SOP and energy storage, combining conventional devices (such as on-load tap changers and capacitor banks) with contemporary devices (such as SOP, distributed generators, and energy storage) to establish synergy. A coordinated optimization model was developed, considering various operational constraints to minimize network losses and regulate the voltage of distribution network nodes. By using linearization and quadratic relaxation, the original non-convex mixed-integer non-linear optimization model was transformed into a Mixed-Integer Second-Order Cone Programming (MISOCP) model to meet the requirements of rapid voltage regulation. Results: A case study was conducted on the IEEE 33-node test system, showing that the proposed approach effectively reduces network losses and eliminates voltage violations. Conclusion: The feasibility and effectiveness of the proposed methodology have been validated, confirming its ability to ensure the safe and economic operation of active distribution networks.

Contrast-preserving image smoothing via the truncated first-order rational function

The main task of image smoothing is to remove the insignificant details of the input image while preserving salient structural edges. In the fields of computer vision and graphics, image smoothing techniques are of great practical importance. In this paper, we investigate a new nonconvex variational optimization model for contrast-preserving image smoothing based on the truncated first-order rational (TFOR) penalty function. We employ an iterative numerical method that utilizes the half-quadratic minimization to effectively solve the proposed model. To validate the effectiveness of the proposed method, we compare it with some related state-of-the-art methods. Experimental results are given to show that the proposed method performs well in preserving the image contrast while maintaining the important edges and structures. We apply the proposed method on various classic image processing tasks such as clip-art compression artifact removal, detail enhancement, image denoising, image abstraction, flash and no-flash image restoration, and guided depth map upsampling.

Sufficient Efficiency Criteria for New Classes of Non-Convex Optimization Models

Sufficient Efficiency Criteria for New Classes of Non-Convex Optimization Models

Pig-DTpV: A prior information guided directional TpV algorithm for orthogonal translation computed laminography

The local scanning orthogonal translation computed laminography (OTCL) has great potential for tiny fault detection of laminated structure thin-plate parts. However, it generates limited-angle and truncated projection data, which result in aliasing and truncation artifacts in the reconstructed images. The directional total variation (DTV) algorithm has been demonstrated to achieve highly accurate reconstructed images in limited-angle computed tomography (CT). However, its application in local scanning OTCL has not been explored. Based on this algorithm, we introduce the lp norm to better suppress artifacts, and prior information to further constrain the reconstructed image. Thus, we propose a prior information guided directional total p-variation (DTpV) algorithm (Pig-DTpV). The Pig-DTpV model is a constrained non-convex optimization model. The constraint term are the six DTpV terms, whereas the objective term is the data fidelity term. Then, we use the iterative reweighting strategy and the Chambolle–Pock (CP) algorithm to solve the model. The Pig-DTpV reconstruction algorithm’s performance is compared with other algorithms such as simultaneous algebraic reconstruction technique (SART), TV, reweighted anisotropic-TV (RwATV), and DTV in simulation and real data experiments. The experiment results demonstrate that the Pig-DTpV algorithm can reduce truncation and aliasing artifacts and enhance the quality of reconstructed images.

Resource-saving scheduling scheme for centralized target tracking in multiple radar system under automatic blanket jamming

This paper investigates the problem of Joint Radar Node Selection and Power Allocation (JRNSPA) in the Multiple Radar System (MRS) in the blanket jamming environment. Each radar node independently tracks moving target and subsequently transmits the raw observation data to the fusion center, which formulates a centralized tracking network structure. In order to establish a practical blanket jamming environment, we suppose that each target carries the self-defense jammer which automatically implements blanket jamming to the radar nodes that exceed the preset interception probability. Subsequently, the Predicted Conditional Cramer-Rao Lower Bound (PC-CRLB) is derived and utilized as the tracking accuracy criterion. Aimed at ensuring both the tracking performance and the Low Probability of Intercept (LPI) performance, the resource-saving scheduling model is formulated to minimize the transmit power consumption while meeting the requirements of tracking accuracy. Finally, the Modified Zoutendijk Method Of Feasible Directions (MZMFD)-based two-stage solution technique is adopted to solve the formulated non-convex optimization model. Simulation results show the effectiveness of the proposed JRNSPA scheme.

Multi-Mission Oriented Joint Optimization of Task Assignment and Flight Path Planning for Heterogeneous UAV Cluster

This paper puts forward a joint optimization algorithm of task assignment and flight path planning for a heterogeneous unmanned aerial vehicle (UAV) cluster in a multi-mission scenario (MMS). The basis of the proposed algorithm is to establish constraint and threat models of a heterogeneous UAV cluster to simultaneously minimize range and maximize value gain and survival probability in an MMS under the constraints of task payload, range, and task requirement. On one hand, the objective function for the heterogeneous UAV cluster within an MMS is derived and it is adopted as a metric for assessing the performance of the joint optimization in task assignment and flight path planning. On the other hand, since the formulated joint optimization problem is a multi-objective, non-linear, and non-convex optimization model due to its multiple decision variables and constraints, the roulette wheel selection (RWS) principle and the elite strategy (ES) are introduced in an ant colony optimization (ACO) to solve the complex optimization model. The simulation results indicate that the proposed algorithm is superior and more efficient compared to other approaches.

Cognitive Radar Waveform Design Method under the Joint Constraints of Transmit Energy and Spectrum Bandwidth

The water-filling (WF) algorithm is a widely used design strategy in the radar waveform design field to maximize the signal-to-interference-plus-noise ratio (SINR). To address the problem of the poor resolution performance of the waveform caused by the inability to effectively control the bandwidth, a novel waveform-related optimization model is established in this paper. Specifically, a corrected SINR expression is first derived to construct the objective function in our optimization model. Then, equivalent bandwidth and energy constraints are imposed on the waveform to formulate the waveform-related non-convex optimization model. Next, the optimal frequency spectrum is obtained using the Karush–Kuhn–Tucker condition of our non-convex model. Finally, the transmit waveform in the time domain is synthesized under the constant modulus constraint. Different experiments based on simulated and real-measured data are constructed to demonstrate the superior performance of the designed waveform on the SINR and equivalent bandwidth compared to the linear frequency modulated signal and waveform designed by the WF algorithm. In addition, to further evaluate the effectiveness of the proposed algorithm in the application of cognitive radar (CR), a closed-loop radar system design strategy is introduced based on our waveform design method. The experiments under real-measured data confirm the advantages of CR compared to the traditional open-loop radar structure.

Directional shadow price in linearly constrained nonconvex optimization models

Directional shadow price in linearly constrained nonconvex optimization models

Local-and-Nonlocal Spectral Prior Regularized Tensor Recovery for Cauchy Noise Removal

Cauchy noise removal in multidimension visual data is a fundamental problem in image processing and data science communities. Recently, this problem can be effectively solved by resorting to an appropriate tensor recovery approach and has attracted increasing attention. However, it is not extensively reported whether tensor recovery approaches with multiple priors can achieve even better denosing performance. To address this issue, we propose a novel tensor recovery approach in this paper based on the maximum a posteriori estimation (MAP). Our approach is a nonconvex optimization model that includes a composite regularization term and a data fidelity term. The composite regularization term incorporates nonlocal self-similarity in the spatial and gradient domains of multidimensional visual data, preserving both local image details and non-local structures. The data fidelity term is obtained by computing the negative log-likelihood of Cauchy noise distribution. To solve this proposed tensor recovery model, we develop an effective denoising algorithm with a global convergence guarantee via the well-known nonconvex alternating direction method of multipliers (ADMM). Finally, we conduct extensive numerical experiments to demonstrate that our proposed recovery approach can achieve superior denoising performance, both quantitatively and qualitatively, compared to existing common methods.

Collaborative Trajectory Planning and Resource Allocation for Multi-Target Tracking in Airborne Radar Networks under Spectral Coexistence

This paper develops a collaborative trajectory planning and resource allocation (CTPRA) strategy for multi-target tracking (MTT) in a spectral coexistence environment utilizing airborne radar networks. The key mechanism of the proposed strategy is to jointly design the flight trajectory and optimize the radar assignment, transmit power, dwell time, and signal effective bandwidth allocation of multiple airborne radars, aiming to enhance the MTT performance under the constraints of the tolerable threshold of interference energy, platform kinematic limitations, and given illumination resource budgets. The closed-form expression for the Bayesian Cramér–Rao lower bound (BCRLB) under the consideration of spectral coexistence is calculated and adopted as the optimization criterion of the CTPRA strategy. It is shown that the formulated CTPRA problem is a mixed-integer programming, non-linear, non-convex optimization model owing to its highly coupled Boolean and continuous parameters. By incorporating semi-definite programming (SDP), particle swarm optimization (PSO), and the cyclic minimization technique, an iterative four-stage solution methodology is proposed to tackle the formulated optimization problem efficiently. The numerical results validate the effectiveness and the MTT performance improvement of the proposed CTPRA strategy in comparison with other benchmarks.

An ADMM Approach of a Nonconvex and Nonsmooth Optimization Model for Low-Light or Inhomogeneous Image Segmentation

In this paper, we propose a novel nonconvex and nonsmooth optimization model for low-light or inhomogeneous image segmentation which is a hybrid of Mumford–Shah energy functional and Retinex theory. The given image is decomposed into the reflectance component and the illumination component by solving Retinex-based Mumford–Shah model with [Formula: see text] regularizer. Indeed, the existence of the [Formula: see text] regularizer means the nonsmooth term in the model is nonconvex. Thus, it is difficult to solve the proposed model directly. An alternating direction method of multipliers (ADMM) algorithm is developed to solve the proposed nonconvex and nonsmooth model. We apply a novel splitting technique in our algorithm to ensure that all subproblems admit closed-form solutions. Theoretically, we prove that the sequence generated by our proposed algorithm converges to a stationary point under mild conditions. Next, once the reflectance is obtained, the [Formula: see text]-means clustering method is utilized to complete the segmentation. We compare the proposed Retinex-based method with other state-of-the-art segmentation methods under special lighting conditions. Experimental results show that the proposed method has better performance for both gray-scale images and color images efficiently in terms of the quantitative and qualitative results.

An Improved DCC Model Based on Large-Dimensional Covariance Matrices Estimation and Its Applications

The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that portfolio is essentially a convex quadratic programming problem, which is also a special case of symmetric cone optimization. Accurate covariance matrix estimation will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence of time-varying factor on the covariance matrix estimations. To remedy this, in this article, we propose an improved dynamic conditional correlation model (DCC) by using nonconvex optimization model under smoothly clipped absolute deviation and hard-threshold penalty functions. We first construct a nonconvex optimization model to obtain the optimal covariance matrix estimation, and then we use this covariance matrix estimation to replace the unconditional covariance matrix in the DCC model. The result shows that the loss of the proposed estimator is smaller than other variants of the DCC model in numerical experiments. Finally, we apply our proposed model to the classic Markowitz portfolio. The results show that the improved dynamic conditional correlation model performs better than the current DCC models.

Security-constrained hybrid optimal energy flow model of multi-energy system considering N-1 component failure

The analysis and calculation of hybrid energy flow is the basis of planning, operation and market transaction of multi-energy systems. An optimal energy flow model of multi-energy systems considering N-1 component failure is proposed in this paper. The compressor and gas storage devices are modeled in the hybrid optimal energy flow model. The particle swarm intelligent optimization algorithm is used to solve this non-convex and non-linear optimization model. Case studies demonstrate the coupled and complementary operation of multi-energy systems can reduce the total operation cost by 8 % as compared to independent operation model. The hybrid optimal energy flow (HOEF) model of multi-energy systems with N-1 component failure can improve the robustness of HOEF results.

A First-Order Primal-Dual Method for Nonconvex Constrained Optimization Based on the Augmented Lagrangian

Nonlinearly constrained nonconvex and nonsmooth optimization models play an increasingly important role in machine learning, statistics, and data analytics. In this paper, based on the augmented Lagrangian function, we introduce a flexible first-order primal-dual method, to be called nonconvex auxiliary problem principle of augmented Lagrangian (NAPP-AL), for solving a class of nonlinearly constrained nonconvex and nonsmooth optimization problems. We demonstrate that NAPP-AL converges to a stationary solution at the rate of [Formula: see text], where k is the number of iterations. Moreover, under an additional error bound condition (to be called HVP-EB in the paper) with exponent [Formula: see text], we further show the global convergence of NAPP-AL. Additionally, if [Formula: see text], then we furthermore show that the convergence rate is in fact linear. Finally, we show that the well-known Kurdyka-Łojasiewicz property and the Hölderian metric subregularity imply the aforementioned HVP-EB condition. We demonstrate that under mild conditions, NAPP-AL can also be interpreted as a variant of the forward-backward operator splitting method in this context. Funding: This work was supported by the National Natural Science Foundation of China [Grant 71871140].

Nonconvex optimization for third‐order tensor completion under wavelet transform

AbstractThe main aim of this paper is to develop a nonconvex optimization model for third‐order tensor completion under wavelet transform. On the one hand, through wavelet transform of frontal slices, we divide a large tensor data into a main part tensor and three detail part tensors, and the elements of these four tensors are about a quarter of the original tensors. Solving these four small tensors can not only improve the operation efficiency, but also better restore the original tensor data. On the other hand, by using concave correction term, we are able to correct for low rank of tubal nuclear norm (TNN) data fidelity term and sparsity of ‐norm data fidelity term. We prove that the proposed algorithm can converge to some critical point. Experimental results on image, magnetic resonance imaging and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state‐of‐the‐arts including the TNN and other methods.

An accelerated alternating directional method with non-monotone technique for matrix recovery

<abstract><p>Low-rank and sparse structures have been frequently exploited in matrix recovery and robust PCA problems. In this paper, we develop an alternating directional method and its variant equipped with the non-monotone search procedure for solving a non-convex optimization model of low-rank and sparse matrix recovery problems, where the concerned matrix with incomplete data is separable into a low-rank part and a sparse part. The main idea is to use the alternating minimization method for the low-rank matrix part, and to use the non-monotone line search technique for the sparse matrix part to iteratively update, respectively. To some extent, the non-monotone strategy relaxes the single-step descent into a multi-step descent and then greatly improves the performance of the alternating directional method. Theoretically, we prove the global convergence of the two proposed algorithms under some mild conditions. Finally, the comparison of numerical experiments shows that the alternate directional method with non-monotone technique is more effective than the original monotone method and the previous method. The efficiency and effectiveness of the proposed algorithms are demonstrated by solving some instances of random incomplete matrix recovery problems and some problems of the background modeling in video processing.</p></abstract>

Hybrid non-convex regularizers model for removing multiplicative noise

Obtaining natural and realistic restorations from the noisy images contaminated by multiplicative noise is a challenging task in image processing. To get over this conundrum, by introducing the non-convex potential functions into the total variation and high-order total variation regularizers, we investigate a novel hybrid non-convex optimization model for image restoration. Numerically, to optimize the resulting high-order PDE system, a proximal linearized alternating minimization method, based on the classical iteratively reweighted ℓ 1 algorithm and variable splitting technique, is designed in detail. Meanwhile, the convergence of the constructed algorithm is also established on the basis of convex analysis. The provided numerical experiments point out that our new scheme shows superiorities in both visual effects and quantitative comparison, especially in terms of the staircase aspects suppression and edge details preservation, compared with some popular denoising methods.

Blind Image Inpainting with Mixture Noise Using ℓ 0 and Total Regularization.

The blind image inpainting problem need to be handle when faced with a large number of images, especially medical images in medical health. For the proposed nonconvex sparse optimization model, a proximal based alternating direction method of multipliers (PADMM) method is designed to solve the problem. Firstly, ℓ0 sparse regularization is imposed to the binary mask since the missing pixels are sparse in our experiments. Secondly, the total variation term is utilized to describe the underlying clean image. Finally, ℓ2 regularization of the fidelity term is used to solve the given blind inpainting problem. Experiments show that this method has better performance than traditional method, and could deal with the blind image inpainting problem.

Alternating direction method of multipliers for nonconvex log total variation image restoration

In this paper, we propose a nonconvex log total variation model for image restoration. A specific alternating direction method of multipliers is also presented to solve the nonconvex optimization model. Under mild conditions, we prove that the sequence generated by the proposed alternating direction method of multipliers converges to a stationary point. Experiment results on image denoising, image deblurring, computed tomography, magnetic resonance imaging and image super-resolution demonstrate that the proposed method is effective and improves the quality of image recovery.

Passenger-Centric Slot Allocation at Schedule-Coordinated Airports

Schedule coordination is the primary form of demand management used at busy airports. At its core, slot allocation involves a highly complex combinatorial problem. In response, optimization models have been developed to minimize the displacement of flight schedules from airline requests, subject to physical and administrative constraints. Existing approaches, however, may not result in the best itineraries for passengers. This paper proposes an original passenger-centric approach to airport slot allocation to maximize available itineraries and minimize connecting times. Because of the uncertainty regarding passenger demand, the proposed approach combines predictive analytics to forecast passenger flows in flight networks from historical data and prescriptive analytics to optimize airport slot assignments in view of flight-centric and passenger-centric considerations. The problem is formulated as a mixed-integer nonconvex optimization model. To solve it, we propose an approximation scheme that alternates between flight-scheduling and passenger-accommodation modules and embed it into a large-scale neighborhood search algorithm. Using real-world data from the Singapore Changi and Lisbon Airports, we show that the proposed model and algorithm return solutions in acceptable computational times. Results suggest that slot-allocation outcomes can be made much more consistent with passenger flows at a relatively small cost in terms of flight displacement. Ultimately, this paper provides a new paradigm that can create more attractive flight schedules by bringing together airport-level considerations, airline-level considerations, and, for the first time, passenger-level considerations. Funding: Financial support from the Civil Aviation Authority of Singapore [Project on Airfield Management and Economics] is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1165 .