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UPrime: Unrolled Phase Retrieval Iterative Method with provable convergence

SIGNAL PROCESSING 2025年 226卷

作者： Shi, Baoshun Gao, Yating Zhang, Runze Yanshan Univ Sch Informat Sci & Engn Qinhuang Dao 066004 Hebei Peoples R China Hebei Key Lab Informat Transmiss & Signal Proc Qinhuang Dao 066004 Hebei Peoples R China

Phase Retrieval (PR) is an ill-posed inverse problem which arises in various science and engineering applications. Recently, it has been empirically shown that unrolled iterative methods or model-driven deep learning methods are effective for solving this problem. However, the prior modules in these model-driven networks lack model interpretability, leading to a lack of rigorous analysis about the convergence behaviors of these re-implemented iterations, and thus the significance of such PR methods is a little bit vague. For this issue, this paper proposes an effective and provable Unrolled Phase Retrieval Iterative MEthod (UPrime) for the PR problem. Our theoretical analysis demonstrates that UPrime using an elaborated bounded prior module can generate fixed-point convergent trajectories. Meanwhile, the proposed prior module, a flexible and interpretable module, is beneficial for the convergence analysis of regularized imaging methods in the non-convex scenario. Experiments on coded diffraction imaging applications verify the superiority of UPrime.

关键词： Phase retrieval non-convex optimization Deep unrolled methods Convergence analysis

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Compliant design of self-dilating vascular stent based on robustness meta-heuristic evolution

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2025年第3期68卷 1-21页

作者： Xu, Jinghua Tao, Mingzhe Wang, Linxuan Er, Taryong Chen, Cheng Wang, Yu Dong, Zhenyu Zhang, Shuyou Zhejiang Univ State Key Lab Fluid Power & Mechatron Syst Hangzhou 310058 Peoples R China Chongqing Univ State Key Lab Mech Transmiss Chongqing 400044 Peoples R China Huazhong Univ Sci & Technol State Key Lab Mat Proc & Die & Mould Technol Wuhan 430074 Peoples R China Zhejiang Univ Zhejiang Key Lab Adv Mfg Technol Hangzhou 310058 Peoples R China Zhejiang Univ Design Engn Inst Hangzhou 310058 Peoples R China Qingdao Huangdao Dist Peoples Hosp Qingdao 266400 Peoples R China

This paper presents a compliant design method of a self-dilating vascular stent based on robustness meta-heuristic evolution (RME). The initial conceptual design prototype of a biodegradable vascular stent is built, comprising a concave hexagonal base structure and a bionic honeycomb shape structure. Bending stiffness and flexibility simulation are carried out to construct the relationship between design variables and compliant performance. The test points used to obtain the initial scheme are generated by the Latin Hypercube Sampling (LHS) method, which can work well in small sample conditions. The Kriging agent is employed to simplify the optimization objective function. To implement non-convex optimization, the rime ice optimization algorithm, enhanced by chaotic mapping and Cauchy variants, is explored to find the global optimum. For the multidisciplinary design issue, the multi-objective optimization (MOO) can further evolve to the Pareto-optimal solutions (POS), using non-dominated sorting method rather than simply weighting method. From the perspective of comparatively verification, more coherent comparisons are examined, including blood flow velocity via hemodynamics simulation, vessel displacement and stress, as well as vascular stents radial displacement with variable narrowing rates. The physical experiment with a case of Peripheral Artery Disease (PAD) in lower limb is provided. The practice indicates that robustness optimization enhances the stent's structural performance and reliability. RME thus has the advantage of efficient optimization convergence under hybrid uncertainty, especially involving multidisciplinary structure optimization.

关键词： Compliant design Self-dilating vascular stent Robustness meta-heuristic evolution (RME) Hemodynamics simulation non-convex optimization

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A Federated Learning Incentive Mechanism for Dynamic Client Participation:Unbiased Deep Learning Models

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Computers, Materials & Continua 2025年第4期83卷 619-634页

作者： Jianfeng Lu Tao Huang Yuanai Xie Shuqin Cao Bing Li School of Computer Science and Technology Wuhan University of Science and TechnologyWuhan430065China College of Computer Science South-Central Minzu UniversityWuhan430074China School of Computer Science and Technology Zhejiang Normal UniversityJinhua321004China

The proliferation of deep learning(DL)has amplified the demand for processing large and complex datasets for tasks such as modeling,classification,and ***,traditional DL methods compromise client privacy by collecting sensitive data,underscoring the necessity for privacy-preserving solutions like Federated Learning(FL).FL effectively addresses escalating privacy concerns by facilitating collaborative model training without necessitating the sharing of raw *** that FL clients autonomously manage training data,encouraging client engagement is pivotal for successful model *** overcome challenges like unreliable communication and budget constraints,we present ENTIRE,a contract-based dynamic participation incentive mechanism for *** ensures impartial model training by tailoring participation levels and payments to accommodate diverse client *** approach involves several key ***,we examine how random client participation impacts FL convergence in non-convex scenarios,establishing the correlation between client participation levels and model ***,we reframe model performance optimization as an optimal contract design challenge to guide the distribution of rewards among clients with varying participation *** balancing budget considerations with model effectiveness,we craft optimal contracts for different budgetary constraints,prompting clients to disclose their participation preferences and select suitable contracts for contributing to model ***,we conduct a comprehensive experimental evaluation of ENTIRE using three real *** results demonstrate a significant 12.9%enhancement in model performance,validating its adherence to anticipated economic properties.

关键词： Federated learning deep learning non-IID data dynamic client participation non-convex optimization contract

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optimization of non-convex Multiband Cooperative Sensing With Genetic Algorithms

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2011年第1期5卷 87-96页

作者： Sanna, Michele Murroni, Maurizio Univ Cagliari Dept Elect & Elect Engn I-09123 Cagliari Italy

In cognitive radios (CRs), secondary users (SUs) transmit alongside primary users (PUs). In order to avoid interference SU perform spectrum sensing and adaptive transmission. Reliable detection in wide geographical regions needs to perform collaborative sensing. The state of the art for efficient cooperative sensing is linear statistics combination. Spatial-spectral joint detection also provides multiband cooperative sensing to access opportunistically several bands at a time. convex maximization is able to solve only an approximation of the optimization within a restricted solution domain, due to its non-convex nature. In this paper, we demonstrate that convex constraints are counterproductive and we propose an alternative optimization technique based on genetic algorithms. The genetic programming performs direct search of the optimal solution one step before the reformulations needed previously. We demonstrate that, by operating directly on the objective and abstracting from the convexity, the collaborative multiband sensing is optimized consistently with the problem formulation.

关键词： Cognitive radio (CR) collaborative sensing cooperative sensing genetic algorithms (GAs) multiband sensing non-convex optimization spectrum sensing wideband sensing

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A tractable approximation of non-convex chance constrained optimization with non-Gaussian uncertainties

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ENGINEERING optimization 2015年第4期47卷 495-520页

作者： Geletu, Abebe Kloeppel, Michael Hoffmann, Armin Li, Pu Tech Univ Ilmenau Inst Automat & Syst Engn Dept Simulat & Optimal Proc D-98684 Ilmenau Germany Tech Univ Ilmenau Inst Math Dept Operat Res & Stochast D-98684 Ilmenau Germany

Chance constrained optimization problems in engineering applications possess highly nonlinear process models and non-convex structures. As a result, solving a nonlinear non-convex chance constrained optimization (CCOPT) problem remains as a challenging task. The major difficulty lies in the evaluation of probability values and gradients of inequality constraints which are nonlinear functions of stochastic variables. This article proposes a novel analytic approximation to improve the tractability of smooth non-convex chance constraints. The approximation uses a smooth parametric function to define a sequence of smooth nonlinear programs (NLPs). The sequence of optimal solutions of these NLPs remains always feasible and converges to the solution set of the CCOPT problem. Furthermore, Karush-Kuhn-Tucker (KKT) points of the approximating problems converge to a subset of KKT points of the CCOPT problem. Another feature of this approach is that it can handle uncertainties with both Gaussian and/or non-Gaussian distributions.

关键词： analytic approximation non-Gaussian distribution non-convex optimization chance constraints

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A hybrid non-linear time-varying double-weighted particle swarm optimization for solving non-convex combined environmental economic dispatch problem

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APPLIED SOFT COMPUTING 2020年 86卷

作者： Goudarzi, Arman Li, Yanjun Xiang, Ji Zhejiang Univ Coll Elect Engn Hangzhou Zhejiang Peoples R China Zhejiang Univ City Coll Sch Informat & Elect Engn Hangzhou Zhejiang Peoples R China

Fossil-fuel based power sources cause environmental pollution such as the degradation of air quality and climate change, which negatively impacts the life on the earth. Consequently, this demands that the power generation should consider the optimal management of thermal sources that are aimed at minimizing the emission of gasses in the generation mix. The production volume of multi-pollutant gasses (SO2, NOx, and CO2) can be reduced through a combined environmental economic dispatch (CEED) approach. This study has proposed a hybrid algorithm based on a novel combination of a modified genetic algorithm and an improved version of particle swarm optimization abbreviated as MGAIPSO to solve CEED problem. The study utilizes three robust operators to enhance the performance of the proposed hybrid algorithm. In GA, a uniformly weighted arithmetic crossover and a normally distributed mutation operator have been implemented to produce elite off-springs in each iteration and diversify the solutions in the search space. In the case of PSO, a non-linear time-varying double-weighted (NLTVDW) technique is developed to obtain a substantial balance between exploration and exploitation. To further enhance the exploitation ability of the MGAIPSO, this study has implemented two movements correctional methods to continuously monitor and amend the position and velocity of the particles. Several numerical case studies ranging from small to large-scale are carried out to validate the practicality of the proposed algorithm. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Combined environmental economic dispatch (CEED) MGAIPSO non-convex optimization Robust constraint handling technique Generators operational constraints

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A robust stochastic quasi-Newton algorithm for non-convex machine learning

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APPLIED INTELLIGENCE 2025年第7期55卷 1-14页

作者： Liu, Hanger Liang, Yuqing Liu, Jinlan Xu, Dongpo Northeast Normal Univ Sch Math & Stat Key Lab Appl Stat MOE Changchun 130024 Peoples R China Changchun Normal Univ Dept Math Changchun 130032 Peoples R China

Stochastic quasi-Newton methods have garnered considerable attention within large-scale machine learning ***, the presence of a stochastic gradient equaling zero poses a significant obstacle to updating the quasi-Newtonmatrix, thereby impacting the stability of the quasi-Newton algorithm. To address this issue, a checkpoint mechanism isintroduced, i.e., checking the value ofskbefore updating the quasi-Newton matrix, which effectively prevents zero incrementsin the optimization variable and enhances algorithmic stability during iterations. Meanwhile, a novel gradient incremental formulation is introduced to satisfy curvature conditions, facilitating convergence for non-convex objectives. Additionally, finite-memory techniques are employed to reduce storage requirements in large-scale machine learning tasks. The last iterationof the proposed algorithm is proven to converge in a non-convex setting, which is better than average and minimum iterationconvergence. Finally, experiments are conducted on benchmark datasets to compare the proposed RSLBFGS algorithm withother popular first and second-order methods, demonstrating the effectiveness and robustness of RSLBFGS

关键词： non-convex optimization Machine learning Stochastic quasi-Newton methods Checkpoint mechanism Gradient incremental form Limited-memory method

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Security-constrained stochastic optimal power flow analysis using optimally reduced scenarios for wind generation

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ELECTRICAL ENGINEERING 2025年 1-23页

作者： Das, Sourav Das, Barsa Barnali Sengupta, Ananyo Natl Inst Technol Rourkela Dept Elect Engn Rourkela 769008 Orissa India

Electrical power scheduling typically occurs in two stages: day-ahead (DA) planning and real-time (RT) balancing. In DA scheduling, generation and reserve capacities are set for the next day, with reserves used to balance power in RT under variable conditions. Due to the emerging need for electricity, power systems often operate in marginal states, increasing the probability of equipment failure (contingencies). These uncertainties make potential changes in network topology;this situation becomes even more challenging in the presence of renewable energy sources (RESs) due to their inherent uncertain nature. If this combined effect of uncertainty is not considered explicitly during scheduling, the network may collapse. This paper presents a security-constrained stochastic optimal power flow (SC-SOPF) method to schedule generation and reserves in systems with high wind penetration. The stochastic nature of wind power is modeled through scenario-generation and scenario-reduction techniques by formulating it as a non-convex optimization problem. The proposed scenario-reduction technique ensures that the moments of the reduced scenario set remain the same as the original one while maximizing the distinct features in each scenario. The aforesaid problem was solved using particle swarm optimization (PSO), genetic algorithm, differential evolution, ant colony optimization, and whale optimization techniques. It is found that the value of the objective function obtained by the PSO is at least 21.08% lower than other evolutionary algorithms. The reduced scenarios are used in a two-stage stochastic SC-SOPF model, solved using the benders decomposition technique with group cuts. The effectiveness of the proposed SC-SOPF is evaluated with respect to the expected load not served (ELNS) during real-time operations. Tests on modified IEEE 9-bus and 39-bus systems show that although the DA cost increases on average by 8.07% for the modified 9-bus system and only by 0.18% for the modi

关键词： Benders decomposition Day-ahead scheduling non-convex optimization Power system security Real-time scheduling Scenario reduction Stochastic programming

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Single-Shot Phase Retrieval Via Gradient-Sparse non-convex Regularization Integrating Physical Constraints

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JOURNAL OF SCIENTIFIC COMPUTING 2025年第3期102卷 1-41页

作者： Chen, Xuesong Li, Fang East China Normal Univ Sch Math Sci Shanghai 200241 Peoples R China East China Normal Univ Sch Math Sci Key Lab MEA Minist Educ Shanghai 200241 Peoples R China East China Normal Univ Shanghai Key Lab PMMP Shanghai 200241 Peoples R China

Measurements of light typically capture amplitude information, often overlooking crucial phase details. This oversight underscores the importance of phase retrieval (PR), essential in biomedical imaging, X-ray crystallography, and microscopy, for reconstructing complex signals from intensity-only measurements. Traditional methods frequently fall short, especially in noisy conditions or when restricted to single-shot measurements. To address these challenges, we introduce a novel model that combines non-convex regularization with physical constraints. The model adopts the smoothly clipped absolute deviation (SCAD) function as a sparsity regularization term for gradients, incorporating fundamental constraints on support and absorption to establish an inverse model. Using the alternating direction method of multipliers (ADMM), we break down the problem into manageable sub-problems, implementing SCAD shrinkage in the complex domain and applying Wirtinger gradient projection methods. A thorough convergence analysis validates the stability and robustness of the algorithm. Extensive simulations confirm significant improvements in reconstruction quality compared to existing methods, with evaluations demonstrating superior performance across various noise levels and parameter settings.

关键词： Phase retrieval SCAD function ADMM Algorithm Wirtinger gradient non-convex optimization

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DualBi: A dual bisection algorithm for non-convex problems with a scalar complicating constraint

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AUTOMATICA 2025年 175卷

作者： Manieri, Lucrezia Falsone, Alessandro Prandini, Maria Politecn Milan Dipartimento Elettron Informaz & Bioingn Via Ponzio 34-5 I-20133 Milan Italy

This paper addresses non-convex constrained optimization problems that are characterized by a scalar complicating constraint. We propose an iterative bisection method for the dual problem (DualBi Algorithm) that recovers a feasible primal solution, with a performance that progressively improves throughout iterations. Application to multi-agent problems with a scalar coupling constraint results in a decentralized resolution scheme where a central unit is in charge of updating the (scalar) dual variable while agents compute their local primal variables. In the case of multi-agent MILPs, simulations showcase the performance of the proposed method compared with state-of-the-art duality-based approaches. (c) 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： non-convex optimization Control of constrained systems Multi-agent systems Duality-based methods Large-scale optimization problems and methods Complex systems management

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