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Packing spheres with quasi-containment conditions

JOURNAL OF GLOBAL OPTIMIZATION 2024年第3期90卷 671-689页

作者： Fischer, Andreas Litvinchev, Igor Romanova, Tetyana Stetsyuk, Petro Yaskov, Georgiy Tech Univ Dresden Inst Numer Math Dresden Germany Autonomous Univ Nuevo Leon Fac Mech & Elect Engn San Nicolas De Los Garza Mexico Natl Acad Sci Ukraine A Pidhornyi Inst Mech Engn Problems Dept Math Modeling & Optimal Design Kharkiv Ukraine Kharkiv Natl Univ Radio Elect Dept Appl Math Kharkiv Ukraine Kharkiv Natl Univ Radio Elect Dept Syst Engn Kharkiv Ukraine Natl Acad Sci Ukraine V M Glushkov Inst Cybernet Dept Nonsmooth Optimizat Methods Kiev Ukraine

A novel sphere packing problem is introduced. A maximum number of spheres of different radii should be placed such that the spheres do not overlap and their centers fulfill a quasi-containment condition. The latter allows the spheres to lie partially outside the given cuboidal container. Moreover, specified ratios between the placed spheres of different radii must be satisfied. A corresponding mixed-integer nonlinear programming model is formulated. It enables the exact solution of small instances. For larger instances, a heuristic strategy is proposed, which relies on techniques for the generation of feasible points and the decomposition of open dimension problems. Numerical results are presented to demonstrate the viability of the approach.

关键词： Packing spheres Nonstandard packing Quasi-containment Ratio condition Mixed-integer nonlinear programming Heuristic Open dimension problem Decomposition technique nonlinear programming

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Control allocation optimization for an over-actuated tandem tiltwing eVTOL aircraft considering aerodynamic interactions

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AEROSPACE SCIENCE AND TECHNOLOGY 2024年 155卷

作者： Yilmaz, Emre German, Brian J. Georgia Inst Technol Sch Aerosp Engn Atlanta GA 30332 USA

This paper describes control allocation strategies for a tandem tiltwing electric vertical take-off and landing (eVTOL) aircraft with distributed propulsion. The control mappings are constructed as local surrogate models that relate the control effectors to the aircraft's aeropropulsive forces and moments across the full flight envelope, including interactional aerodynamics effects. Control allocation optimization problems are formulated based on force and moment commands for specific flight conditions. Specifically, a nonlinear programming formulation based on nonlinear control mapping is proposed for control allocation optimization, and the problem is solved using a sparse nonlinear optimizer. The solutions obtained from different formulations such as the minimization of force and moment residuals and the minimization of control effort are investigated. Furthermore, these solutions are compared with the solutions obtained using linear control mapping-based formulations. Results presented for the cases of forward flight, low speed flight & hover, and flight in the transition corridor suggest that considering aerodynamic interactions while formulating and solving the control allocation problem is necessary for higher levels of accuracy compared to linear approaches. One-propeller-out scenarios and moment and force generation cases are also investigated. Finally, control allocation for steady and accelerated operation in the transition corridor is discussed. The contribution of the methods and results in the paper is a nonlinear control allocation methodology for the entire flight envelope of an over-actuated tandem tiltwing eVTOL aircraft.

关键词： Control allocation Tiltwing eVTOL aircraft Aerodynamic interactions nonlinear programming Constrained optimization

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Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems

IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2024年 10卷 399-414页

作者： Lyons, Carter Raj, Raghu G. Cheney, Margaret US Naval Res Lab Washington DC 20375 USA Colorado State Univ Ft Collins CO 80523 USA

Incorporating prior information into inverse problems, e.g. via maximum-a-posteriori estimation, is an important technique for facilitating robust inverse problem solutions. In this paper, we devise two novel approaches for linear inverse problems that permit problem-specific statistical prior selections within the compound Gaussian (CG) class of distributions. The CG class subsumes many commonly used priors in signal and image reconstruction methods including those of sparsity-based approaches. The first method developed is an iterative algorithm, called generalized compound Gaussian least squares (G-CG-LS), that minimizes a regularized least squares objective function where the regularization enforces a CG prior. G-CG-LS is then unrolled, or unfolded, to furnish our second method, which is a novel deep regularized (DR) neural network, called DR-CG-Net, that learns the prior information. A detailed computational theory on convergence properties of G-CG-LS and thorough numerical experiments for DR-CG-Net are provided. Due to the comprehensive nature of the CG prior, these experiments show that DR-CG-Net outperforms competitive prior art methods in tomographic imaging and compressive sensing, especially in challenging low-training scenarios.

关键词： Machine learning deep neural networks inverse problems nonlinear programming least squares methods

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Compact Optimization Learning for AC Optimal Power Flow

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第2期39卷 4350-4359页

作者： Park, Seonho Chen, Wenbo Mak, Terrence W. K. Van Hentenryck, Pascal Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

This article reconsiders end-to-end learning approaches to the Optimal Power Flow (OPF). Existing methods, which learn the input/output mapping of the OPF, suffer from scalability issues due to the high dimensionality of the output space. This article first shows that the space of optimal solutions can be significantly compressed using principal component analysis (PCA). It then proposes COMPACT LEARNING, a new method that learns in a subspace of the principal components and translates the vectors into the original output space. This compression reduces the number of trainable parameters substantially, improving scalability and effectiveness. COMPACT LEARNING is evaluated on a variety of test cases from the PGLib and a realistic French transmission system having renewable energy changes with up to 30,000 buses. The article also shows that the output of COMPACT LEARNING can be used to warm-start an exactACsolver to restore feasibility, while bringing significant speed-ups.

关键词： Deep learning end-to-end learning generalized hebbian algorithm nonlinear programming optimal power flow principal component analysis

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Dealing with Multiple Water Uses and Infeasibilities in Complex Hydrothermal System Optimization

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2024年第1期150卷 05023019-05023019页

作者： Falcetta, Filipe Antonio Marques Zambon, Renato Carlos de Barros, Mario Thadeu Leme Yeh, William W. -G. Univ Sao Paulo Inst Energy & Environm BR-05508010 Sao Paulo SP Brazil Univ Sao Paulo Polytech Sch Dept Hydraul & Environm Engn BR-05508010 Sao Paulo SP Brazil Univ Calif Los Angeles Dept Civil & Environm Engn Los Angeles CA 90095 USA

Severe droughts, water-use conflicts, and minimum outflow requirements have caused infeasibilities in modeling large-scale complex hydrothermal systems. This paper presents and discusses a new formulation of objective function and constraints to better represent multiple water uses and deal with infeasibilities in the HIDROTERM model, a nonlinear programming (NLP) model developed to optimize the operation of the Brazilian interconnected hydrothermal system. The system is one of the largest in the world. In the last 10 years, approximately 72% of electricity consumed in Brazil has been supplied by hydropower plants, but with increasing shares from thermal, wind, and, more recently, solar power generation. Because of hydrological changes in recent years and the additional operational constraints imposed by environmental agencies, the use of models for decision making, such as HIDROTERM, frequently encounters the problem of infeasibility. To avoid this problem, a new objective function is proposed in HIDROTERM that incorporates economic penalties when the preset requirements are not met. Based on economic considerations, some hard constraints are removed from the constraint set and added to the objective function as penalty terms. These constraints are tightly linked with multiple water uses, including environmental protection, flood control, consumptive uses, and navigation purposes. The proposed change in the objective function and constraints avoids the problem of infeasibilities and makes it possible to apply the model to extreme conditions. Additionally, this formulation helps identify and minimize the risk, duration, and intensity of unavoidable non-compliance occurrences related to multiple water uses. The presented new version of the HIDROTERM model can be used to study and support decision making in the management and operation of large-scale hydrothermal systems. These systems can be formed by a set of hydraulically connected individual hydropower plants and

关键词： Hydropower Reservoir operation Optimization nonlinear programming

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Adaptive safety-critical control for a class of nonlinear systems with parametric uncertainties: A control barrier function approach

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SYSTEMS & CONTROL LETTERS 2024年 188卷

作者： Wang, Yujie Xu, Xiangru Univ Wisconsin Madison Dept Mech Engn Madison WI 53706 USA

This paper presents a novel approach for the safe control design of systems with parametric uncertainties in both drift terms and control -input matrices. The method combines control barrier functions and adaptive laws to generate a safe controller through a nonlinear program with an explicitly given closed -form solution. The proposed approach verifies the non -emptiness of the admissible control set independently of online parameter estimations, which can ensure that the safe controller is singularity -free. A data -driven algorithm is also developed to improve the performance of the proposed controller by tightening the bounds of the unknown parameters. The effectiveness of the control scheme is demonstrated through numerical simulations.

关键词： Safety-critical control Control barrier functions Adaptive control Data-driven approach nonlinear programming

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Multi-Phase Trajectory Optimization for Alpine Skiers Using an Improved Retractable Body Model

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第3期201卷 1063-1088页

作者： Cai, Congying Yao, Xiaolan Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China

In this paper, an improved retractable body model (IRBM) is established, which has an advantage in simulating the flexion-and-extension motion of skier's legs during carved turning and straight gliding. The trajectory optimization problem for the nonlinear alpine skiing system is transformed into a multi-phase optimal control (MPOC) problem. Subsequently, a constrained multi-phase trajectory optimization model is developed based on the optimal control theory, where the optimization target is to minimize the total skiing time. The optimization model is discretized by using the Radau pseudospectral method (RPM), which transcribes the MPOC problem into a nonlinear programming (NLP) problem that is then solved by SNOPT solver. Through numerical simulations, the optimization results under different constraints are obtained using MATLAB. The variation characteristics of the variables and trajectories are analyzed, and four influencing factors related to the skiing time are investigated by comparative experiments. It turns out that the small turning radius can reduce the total skiing time, the flexion-and-extension motion of legs is beneficial to skier's performance, and the large inclination angle can shorten skier's turning time, while the control force has a slight effect on the skiing time. The effectiveness and feasibility of the proposed models and trajectory optimization strategies are validated by simulation and experiment results.

关键词： Improved retractable body model nonlinear alpine skiing system Multi-phase trajectory optimization Optimal control nonlinear programming

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Modelling a capacitated location problem for designing multimodal vaccine distribution network using a novel Health Emergency Susceptibility Index

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COMPUTERS & OPERATIONS RESEARCH 2025年 180卷

作者： Kar, Biswajit Jenamani, Mamata Indian Inst Technol Dept Ind & Syst Engn Kharagpur 721302 W Bengal India

Health emergency due to the outbreak of a contagious virus augments the need for effective vaccine distribution strategies to control its spread. This paper suggests a two-phase strategy to solve this problem. Phase I constructs a Health Emergency Susceptibility Index for each region, considering the disease data and comorbidity situation. Phase II uses the HESI and proposes three versions of priority weights for different application scenarios. These are used as the priority weights to formulate a capacitated location problem with a multimodal network and multiple types of refrigerators. The model considers additional factors like storage capacity, locations, transportation distances (including air and ground options), costs (maintenance and transportation), and vehicle capacity. To solve the model for large networks, the paper suggests a solution approach using Benders Decomposition with extreme directions. To validate the models, we examine the case of COVID-19 vaccine distribution in India. To assess the impact of the Susceptibility Index on facility locations, proposed weightage versions are compared with a version that does not use the index. The results show that one of the three versions with weighting schemes based on the population-to-susceptibility ratio leads to the most cost-effective distribution strategy, ensuring coverage of all susceptible regions. Furthermore, the Decomposition-based solution significantly improves computational efficiency, solving the problem over fifty times faster than the commercial solver.

关键词： SIR model Healthcare Facility location nonlinear programming P-Centre problem Priority distribution MIQCP

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Accelerated first-order optimization under nonlinear constraints

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MATHEMATICAL programming 2025年 1-46页

作者： Muehlebach, Michael Jordan, Michael I. Max Planck Inst Intelligent Syst Learning & Dynam Syst Max Planck Ring 4 D-72076 Tubingen Baden Wuerttemb Germany Univ Calif Berkeley Dept Elect Engn & Comp Sci 387 Soda Hall Berkeley CA 94720 USA

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected gradients, these algorithms avoid optimization over the entire feasible set at each iteration. We prove convergence to stationary points even in a nonconvex setting and we derive accelerated rates for the convex setting both in continuous time, as well as in discrete time. An important property of these algorithms is that constraints are expressed in terms of velocities instead of positions, which naturally leads to sparse, local and convex approximations of the feasible set (even if the feasible set is nonconvex). Thus, the complexity tends to grow mildly in the number of decision variables and in the number of constraints, which makes the algorithms suitable for machine learning applications. We apply our algorithms to a compressed sensing and a sparse regression problem, showing that we can treat nonconvex & ell;(p) constraints (p<1) efficiently, while recovering state-of-the-art performance for p=1.

关键词： Constrained optimization nonlinear programming Gradient-based methods Machine learning

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APPLICATIONS OF MATHEMATICAL programming TO GENETIC BIOCONTROL

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SIAM JOURNAL ON APPLIED MATHEMATICS 2024年第3期84卷 S392-S411页

作者： Vasquez, Valeri n. Marshall, John m. Univ Calif Berkeley Sch Publ Hlth Div Epidemiol & Biostat Berkeley CA 94704 USA

We review existing approaches to optimizing the deployment of genetic biocontrol technologies---tools used to prevent vector-borne diseases such as malaria and dengue---and formulate a mathematical program that enables the incorporation of crucial ecological and logistical details. The model is comprised of equality constraints grounded in discretized dynamic population equations, inequality constraints representative of operational limitations including resource restrictions, and an objective function that jointly minimizes the count of competent mosquito vectors and the number of transgenic organisms released to mitigate them over a specified time period. We explore how nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) can advance the state of the art in designing the operational implementation of three distinct transgenic public health interventions, two of which are presently in active use around the world.

关键词： nonlinear programming mixed integer programming biomathematics dynamic population model genetic modification technology public health vector-borne disease

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