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Convergence of a special partially augmented Lagrangian algorithm for sparsity-constrained optimization problems

OPTIMIZATION LETTERS 2025年 1-16页

作者： Xue, Menglong Pang, Liping Zhejiang Univ Sch Management Hangzhou 310058 Zhejiang Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Liaoning Peoples R China Key Lab Computat Math & Data Intelligence Liaoning Dalian 116024 Liaoning Peoples R China

In this paper, we consider the continuous relaxation reformulation of sparsity-constrained optimization problems. Based on the structure of the relaxation problem, a special partially augmented Lagrangian method is proposed. Unlike the classical approach, this algorithm preserves complementarity-type constraints in the augmented Lagrangian subproblems. Under mild conditions that do not depend on constraint qualification and do not require the multiplier sequence to be bounded, we prove that the arbitrary feasible limit point of the algorithm is sparse constraints positive complementary approximately Mordukhovich stationary, which is currently the strongest approximate stationary point for sparsity-constrained optimization problems.

关键词： Sparsity-constrained optimization problems Sequential optimality conditions nonlinear programming Partially augmented Lagrangian algorithm

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Why fixing alpha in the NRTL model might be a bad idea - Identifiability analysis of binary vapor-liquid equilibria

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CHEMICAL ENGINEERING SCIENCE 2025年 305卷

作者： Kozachynskyi, Volodymyr Hoffmann, Christian Esche, Erik Tech Univ Berlin Proc Dynam & Operat Grp Str 17 Juni 135 D-10623 Berlin Germany

New vapor-liquid equilibrium (VLE) data are continuously being measured and new parameter values, e.g., for the nonrandom two-liquid (NRTL) model are estimated and published. The parameter a , the nonrandomness parameter of NRTL, is often not estimated but is heuristically fixed to a constant value based on the involved components. This can be seen as a manual application of a (subset selection) regularization method. In this work, the practical parameter identifiability of the NRTL model for describing the VLE is analyzed. It is shown that fixing a is not always a good decision and sometimes leads to worse prediction properties of the final parameter estimates. Popular regularization techniques are compared and Generalized Orthogonalization is proposed as an alternative to this heuristic. In addition, the sequential Optimal Experimental Design and Parameter Estimation (sOED-PE) method is applied to study the influence of the regularization methods on the performance of the sOED-PE loop.

关键词： Parameter estimation Model-based optimal experimental design nonlinear programming NRTL VLE

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Unified Incremental nonlinear Controller for the Transition Control of a Hybrid Dual-Axis Tilting Rotor Quad-Plane

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IEEE TRANSACTIONS ON ROBOTICS 2025年 41卷 306-325页

作者： Mancinelli, Alessandro Remes, Bart D. W. de Croon, Guido C. H. E. Smeur, Ewoud J. J. Delft Univ Technol Fac Aerosp Engn NL-2629HS Delft Zuid Holland Netherlands

Hybrid overactuated tilt rotor uncrewed aerial vehicles (TRUAVs) are a category of versatile UAVs known for their exceptional wind resistance capabilities. However, their extensive operational range, combined with thrust vectoring capabilities, presents complex control challenges due to nonaffine dynamics and the necessity to coordinate lift and thrust for controlling accelerations at varying airspeeds. Traditionally, these vehicles rely on switched logic controllers with two or more intermediate states to control transitions. In this study, we introduce an innovative, unified incremental nonlinear controller designed to seamlessly control an overactuated dual-axis tilting rotor quad-plane throughout its entire flight envelope. Our controller is based on an incremental nonlinear control allocation algorithm to simultaneously generate pitch and roll commands, along with physical actuator commands. The control allocation problem is solved using a sequential quadratic programming (SQP) iterative optimization algorithm making it well-suited for the nonlinear actuator effectiveness typical of thrust vectoring vehicles. The controller's design integrates desired roll and pitch angle inputs. These desired attitude angles are managed by the controller and then conveyed to the vehicle during slow airspeed phases, when the vehicle maintains its 6-degrees of freedom (6-DOF). As the airspeed increases, the controller seamlessly shifts its focus to generating attitude commands for lift production, consequently smoothly disregarding the desired roll and pitch angles. Furthermore, our controller integrates an angle of attack (AoA) protection logic to mitigate wing stalling risks during transitions. It also features a yaw rate reference model to enable coordinated turns and minimize side-slip. The effectiveness of our proposed control technique has been confirmed through comprehensive flight tests. These tests demonstrated the successful transition from hovering flight to forward f

关键词： Rotors Actuators Resource management Vectors Attitude control Vehicle dynamics Heuristic algorithms Autonomous aerial vehicles 6-DOF Servomotors Control allocation fully actuated vehicles hybrid UAV incremental nonlinear dynamic inversion (INDI) nonlinear programming quad-plane quadratic programming tilt rotor uncrewed aerial vehicle (UAV) vertical takeoff and landing (VTOL) weighted least squares

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Comprehensive water quality indicators modeling by environmental protection view using multi optimized weighted ensemble machine learnings

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PROCESS SAFETY AND ENVIRONMENTAL PROTECTION 2025年 193卷 696-709页

作者： Poursaeid, Mojtaba Payame Noor Univ Dept Civil Engn Khorramabad Lorestan Iran

The environmental protection water quality is a critical subject in dominance of the sustainable water resources management. Accordingly, the essential indicators of water quality were considered, which are not only appropriate indicators for water quality, but they can also serve as crucial indicators for the health of water environment and ecosystems. Therefore, this study uses well-known ensemble machine learning methodologies to investigate and predict the fluctuations of water quality parameters. Optimization procedures used to assemble machine learnings were non-linear programming (NLP), genetic, gradient descent, and least square algorithms, linear programming, particle swarm optimization, Nelder-Mead optimization, and simulating annealing optimization. Using optimization procedures, the basic MLs were assembled and eight new ensemble machine learning were developed. The studied area was the South Platte River basin, USA. The primary dataset was obtained through the online database of the United States Geological Survey, which contained sampling information on river water related to 2023-2024. Then, using clean missing and outlier data preprocessing techniques, the dataset was modified. Finally, using the 10-fold cross-validation technique, the primary data was validated. The results showed that NLP significantly improved the accuracy and performance of models, achieving the best performance with R2 of 0.9836 and 0.9031 across DO and pH modelings. The modeling results indicated that the pH parameter fluctuated within the safe range. While the DO seems that tolerated in unsafe domain for aquatic ecosystems. The findings of this research could help a wide range of decision-makers.

关键词： Water quality Ensemble machine learning nonlinear programming Linear programming Nelder Mead Simulating annealing

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On Stationarity Conditions and Constraint Qualifications for Multiobjective Optimization Problems with Cardinality Constraints

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APPLIED MATHEMATICS AND OPTIMIZATION 2025年第1期91卷 1-26页

作者： Garmanjani, Rohollah Krulikovski, Evelin H. M. Ramos, Alberto NOVA Sch Sci & Technol NOVA FCT Ctr Math & Applicat NOVA Math Caparica Portugal Univ Fed Parana Dept Math Curitiba Brazil Univ Tarapaca Dept Matemat Casilla 7D Arica Chile

The purpose of this paper is to develop Pareto optimality conditions and constraint qualifications (CQs) for Multiobjective Programs with Cardinality Constraints (MOPCaC). In general, such problems are difficult to solve, not only because they involve a cardinality constraint that is neither continuous nor convex, but also because there may be a potential conflict between the various objective functions. Thus, we reformulate the MOPCaC based on the problem with continuous variables, namely the relaxed problem. Furthermore, we consider different notions of optimality (weak/strong Pareto optimal solutions). Thereby, we define new stationarity conditions that extend the classical Karush-Kuhn-Tucker (KKT) conditions of the scalar case. Moreover, we also introduce new CQs, based on the recently defined multiobjective normal cone, to ensure compliance with such stationarity conditions. Important statements are illustrated by examples.

关键词： Multiobjective optimization Cardinality constraints nonlinear programming Sparse solutions Constraint qualifications Stationarity

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Ponzi system dynamics: time to bankruptcy, optimal bailout time and a condition for survival

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2025年

作者： Parlar, M. McMaster Univ DeGroote Sch Business Hamilton ON L8S 4M4 Canada

Every Ponzi 'investment' scheme is fraudulent and it is destined for eventual collapse. When a Ponzi scheme starts, the early investors make unreasonably high profits from receiving unrealistically high (and 'guaranteed') returns. However, unbeknown to the unsuspecting investors, these returns are made possible not by the profits of a successful business (as claimed by the Ponzi operator), but by the deposits of the later investors. Unfortunately for the later investors, either the money runs out, or the operator disappears. In this paper we analyse the time-dependent progress of the Ponzi scheme using a system of two difference (and later, differential) equations. We estimate the time to bankruptcy (and optimal bailout time for the operator) under several assumptions, including constant, time-varying, random deposit amounts by the investors. An optimal control model to maximise the final time cash balance is also included. We provide a simple (but unusual) condition under which the Ponzi scheme may never go bankrupt. Our results could be of potential benefit to investors to warn them not to be fooled by the promises of a Ponzi scheme fraudster;and if they have invested in such a scheme, to cash out before the scheme collapses or the promoter disappears.

关键词： Ponzi scheme difference equations optimisation stochastic analysis differential equations nonlinear programming Optimisation Quadratic programming Stochastic Systems Systems Continuous-timeSystems

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A modified extended Fletcher-Reeves conjugate gradient method with an application in image restoration

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2025年第6期102卷

作者： Diphofu, T. Kaelo, P. Univ Botswana Dept Math Private Bag UB00704 Gaborone Botswana

In this paper, we propose a modified Fletcher-Reeves conjugate gradient method. The new search direction is calculated in such a way that it is close to a three term PRP conjugate gradient method. In particular, we introduce a parameter that adjusts the weight applied to the standard FR method, ensuring that our CG method satisfies the sufficient descent property. Global convergence is established under the strong Wolfe line search. The method is tested on a set of unconstrained optimization problems and the results demonstrate the new method's competency against existing methods. Furthermore, the new method is implemented to solve an image restoration problem of removing impulse noise from a digital image.

关键词： Conjugate gradient global convergence nonlinear programming image restoration sufficient descent

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Optimizing temperature and pressure in PEM electrolyzers: A model-based approach to enhanced efficiency in integrated energy systems

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ENERGY CONVERSION AND MANAGEMENT 2025年 325卷

作者： Bornemann, Luka Lange, Jelto Kaltschmitt, Martin Hamburg Univ Technol Inst Environm Technol & Energy Econ Eissendorfer Str 40 D-21073 Hamburg Germany

Hydrogen stands as a promising energy carrier within the ongoing energy supply transformation, yet its production via electrolyzers remains prohibitively costly. To address this challenge, this paper proposes an advanced equation-oriented process model fora PEM (Polymer-Electrolyte-Membrane) electrolysis system, including the electrolyzer and downstream hydrogen compression, aimed at optimizing the interaction of its operating parameters (i.e., current density, temperature, pressure). Initially, the model is utilized to analyze the isolated performance of the electrolysis system through operational flowsheet optimizations, followed by its integration into a broader energy system for operational planning optimization. The study reveals several key findings: optimizing operational parameters, rather than using fixed values at the maximum, improves peak system efficiency by approximately 5 %pt. and shifts this peak to lower current densities, thus expanding the range of high-efficiency operation. Each current density has an optimal pair of temperature and pressure, with maximum temperatures only advantageous at loads above 40%, while maximum operating pressure is suboptimal across the entire load range. The analysis indicates that incorporating operating parameter optimization within the operational planning of the electrolysis system reduces energy consumption by 4% and operating costs by 7% in the evaluated energy system. Additionally, the study distinguishes between optimizing the electrolyzer's operating parameters for maximizing its own efficiency and for system efficiency (i.e., including hydrogen compression). It demonstrates that maximum system efficiency is achievable only when the electrolyzer considers hydrogen compression in its operation mode, accepting some efficiency losses individually but yielding greater efficiency gains in the context of hydrogen compression. In summary, the findings of this paper suggest that continuously operating a PEM electrolyze

关键词： Green hydrogen Polymer-electrolyte-membrane electrolyzer Energy system optimization Process optimization nonlinear programming

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Mixed-integer linearity in nonlinear optimization: a trust region approach

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OPTIMIZATION LETTERS 2025年 1-22页

作者： De Marchi, Alberto Univ Bundeswehr Munich Inst Appl Math & Sci Comp Dept Aerosp Engn Werner Heisenberg Weg 39 D-85577 Neubiberg Germany

Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential mixed-integer linearization with trust region safeguard, computing feasible iterates via calls to a generic mixed-integer linear solver. Convergence to critical, possibly suboptimal, feasible points is established for arbitrary starting points. Finally, we present numerical applications in nonsmooth optimal control and optimal network design and operation.

关键词： Mixed-integer programming nonlinear programming Successive linearization schemes Trust region methods

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Distributed model predictive control for consensus of nonlinear systems via parametric sensitivity

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ISA TRANSACTIONS 2025年 156卷 87-98页

作者： Yu, Tianyu Zhao, Fei Xu, Zuhua Zhao, Jun Chen, Xi Zhejiang Univ Coll Control Sci & Engn State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China

To handle the nonlinear consensus problem, a distributed model predictive control (DMPC) scheme is developed via parametric sensitivity. A two-stage input computation strategy is adopted for enhancing optimization efficiency. In the background stage, each agent first establishes its next-step optimization problem based on communication topology, and then performs distributed optimization to calculate the future inputs. In the online stage, all the agents build their sensitivity equations based on new information. Three variants of sensitivity equation are developed based on the level of communication load capacity, and the corresponding computation strategies are proposed. After solution, the background inputs are corrected and implemented. The optimality and robustness of the proposed algorithm are rigorously derived. Finally, the superiority of this DMPC scheme is demonstrated in the multi-vehicle system with two different topologies.

关键词： Consensus problem Distributed model predictive control nonlinear programming Parametric sensitivity

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