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SMOP: Stochastic trust region method for multi-objective problems

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arXiv 2025年

作者： Krejić, Nataša Jerinkić, Nataša Krklec Rutešić, Luka Department of Mathematics and Informatics Faculty of Sciences University of Novi Sad Trg Dositeja Obradovića 4 Novi Sad21000 Serbia

The problem considered is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust region framework with probabilistic model functions, able to cope with noisy problems, using inaccurate functions and gradients. We prove the almost sure convergence of the proposed algorithm to a Pareto critical point if the model functions are good approximations in probabilistic sense. Numerical results demonstrate effectiveness of the probabilistic trust region by comparing it to competitive stochastic multi-objective solvers. The application in supervised machine learning is showcased by training non discriminatory Logistic Regression models on different size data groups. Additionally, we use several test examples with irregularly shaped fronts to exhibit the efficiency of the algorithm. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Convergence towards a local minimum by direct search methods with a covering step

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arXiv 2024年

作者： Bouchet, Pierre-Yves Audet, Charles Bourdin, Loïc École Polytechnique de Montréal MontréalQCH3T 1J4 Canada GERAD MontréalQCH3T 1J4 Canada XLIM Research Institute University of Limoges France

This paper introduces a new step to the Direct Search Method (DSM) to strengthen its convergence analysis. By design, this so-called covering step may ensure that, for all refined points of the sequence of incumbent solutions generated by the resulting cDSM (covering DSM), the set of all evaluated trial points is dense in a neighborhood of that refined point. We prove that this additional property guarantees that all refined points are local solutions to the optimization problem. This new result holds true even for a discontinuous objective function, under a mild assumption that we discuss in details. We also provide a practical construction scheme for the covering step that works at low additional cost per iteration. Finally, we show that the covering step may be adapted to classes of algorithms differing from the DSM. © 2024, CC BY.

关键词： optimization algorithms

HIERARCHICAL MINIMUM VARIANCE PORTFOLIOS: A THEORETICAL AND ALGORITHMIC APPROACH

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arXiv 2025年

作者： Mograby, Gamal Department of Mathematical Sciences University of Cincinnati United States

We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by López de Prado’s hierarchical risk parity and Cotton’s Schur complement methods, our framework models the covariance matrix as an adjacency-like structure of a hierarchical graph. We demonstrate that portfolio optimization can be recursively reduced across hierarchical levels, allowing optimal weights to be computed efficiently by inverting only small submatrices regardless of portfolio size. Moreover, we translate our results into a recursive algorithm that constructs optimal portfolio allocations. Our results reveal a transparent and mathematically rigorous connection between classical Markowitz mean-variance optimization, hierarchical clustering, and the Schur complement *** Codes ***, ***, *** © 2025, CC BY-NC-ND.

关键词： optimization algorithms

Nesterov’s method of dichotomy via Order Oracle: The problem of optimizing a two-variable function on a square

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arXiv 2024年

作者： Chervonenkis, Boris Krasnov, Andrei Gasnikov, Alexander Lobanov, Aleksandr Moscow Institute of Physics and Technology Russia Institute for Information Transmission Problems RAS Moscow Russia Innopolis University Russia Skolkovo Institute of Science and Technology Russia The Institute for System Programming The Russian Academy of Sciences Russia

The challenges of black box optimization arise due to imprecise responses and limited output information. This article describes new results on optimizing multivariable functions using an Order Oracle, which provides access only to the order between function values and with some small errors. We obtained convergence rate estimates for the one-dimensional search method (golden ratio method) under the condition of oracle inaccuracy, as well as convergence results for the algorithm on a "square" (also with noise), which outperforms its alternatives. The results obtained are similar to those in problems with oracles providing significantly more information about the optimized function. Additionally, the practical application of the algorithm has been demonstrated in maximizing a preference function, where the parameters are the acidity and sweetness of the drink. This function is expected to be convex or at least quasi-convex. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

TERIME: An improved RIME algorithm with enhanced exploration and exploitation for robust parameter extraction of photovoltaic models

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arXiv 2024年

作者： Chen, Shi-Shun Jiang, Yu-Tong Chen, Wen-Bin Li, Xiao-Yang School of Reliability and Systems Engineering Beihang University Beijing100191 China

Parameter extraction of photovoltaic (PV) models is crucial for the planning, optimization, and control of PV systems. Although some methods using meta-heuristic algorithms have been proposed to determine these parameters, the robustness of solutions obtained by these methods faces great challenges when the complexity of the PV model increases. The unstable results will affect the reliable operation and maintenance strategies of PV systems. In response to this challenge, an improved RIME algorithm with enhanced exploration and exploitation is proposed for robust and accurate parameter identification for various PV models. Specifically, the differential evolution mutation operator is integrated in the exploration phase to enhance the population diversity. Meanwhile, a new exploitation strategy incorporating randomization and neighborhood strategies simultaneously is developed to maintain the balance of exploitation width and depth. The improved RIME algorithm is applied to estimate the optimal parameters of the single-diode model (SDM), double-diode model (DDM), and triple-diode model (TDM) combined with the Lambert-W function for three PV cell and module types including RTC France, Photo Watt-PWP 201 and S75. According to the statistical analysis in 100 runs, the TEIMRE achieves more accurate and robust parameter estimations than other techniques to various PV models in varying environmental conditions. All of our source codes are publicly available at https://***/dirge1/TERIME. © 2024, CC BY.

关键词： optimization algorithms

A survey on pioneering metaheuristic algorithms between 2019 and 2024

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arXiv 2024年

作者： Dokeroglu, Tansel Canturk, Deniz Kucukyilmaz, Tayfun TED University Software Engineering Department Ankara Turkey Department of Technology and Operations Management Erasmus University Netherlands

This review examines over 150 new metaheuristics of the last six years (between 2019-2024), underscoring their profound influence and performance. Over the past three decades, more than 500 new metaheuristic algorithms have been proposed, with no slowdown in sight—an overwhelming abundance that complicates the process of selecting and assessing the most effective solutions for complex optimization challenges. Our evaluation centers on pivotal criteria, including annual citation metrics, the breadth of addressed problem types, source code availability, user-friendly parameter configurations, innovative mechanisms and operators, and approaches designed to mitigate traditional metaheuristic issues such as stagnation and premature convergence. We further explore recent high-impact applications of the past six years’ most influential 23 metaheuristic algorithms, shedding light on their advantages and limitations, while identifying challenges and potential avenues for future research. © 2024, CC BY.

关键词： optimization algorithms

Partition Constraints for Conjunctive Queries: Bounds and Worst-Case Optimal Joins

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arXiv 2025年

作者： Deeds, Kyle Merkl, Timo Camillo University of Washington SeattleWA United States TU Wien Vienna Austria

In the last decade, various works have used statistics on relations to improve both the theory and practice of conjunctive query execution. Starting with the AGM bound which took advantage of relation sizes, later works incorporated statistics like functional dependencies and degree constraints. Each new statistic prompted work along two lines;bounding the size of conjunctive query outputs and worst-case optimal join algorithms. In this work, we continue in this vein by introducing a new statistic called a partition constraint. This statistic captures latent structure within relations by partitioning them into sub-relations which each have much tighter degree constraints. We show that this approach can both refine existing cardinality bounds and improve existing worst-case optimal join algorithms. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Subgradient Method for System Identification with Non-Smooth Objectives

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arXiv 2025年

作者： Yalcin, Baturalp Lavaei, Javad University of California Berkeley United States

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting where the optimization problems to be solved change over time as new measurements are taken, and we establish linear convergence results for both the best and Polyak step sizes after a burn-in period. Additionally, we characterize the asymptotic convergence of the best average sub-optimality gap under diminishing and constant step sizes. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth *** Codes 62, 90, 93 © 2025, CC BY-NC-ND.

关键词： optimization algorithms

Exploiting Negative Curvature in Conjunction with Adaptive Sampling: Theoretical Results and a Practical Algorithm

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arXiv 2024年

作者： Berahas, Albert S. Bollapragada, Raghu Dong, Wanping Department of Industrial and Operations Engineering University of Michigan United States Operations Research and Industrial Engineering Program University of Texas at Austin United States

In this paper, we propose algorithms that exploit negative curvature for solving noisy nonlinear nonconvex unconstrained optimization problems. We consider both deterministic and stochastic inexact settings, and develop two-step algorithms that combine directions of negative curvature and descent directions to update the iterates. Under reasonable assumptions, we prove second-order convergence results and derive complexity guarantees for both settings. To tackle large-scale problems, we develop a practical variant that utilizes the conjugate gradient method with negative curvature detection and early stopping to compute a step, a simple adaptive step size scheme, and a strategy for selecting the sample sizes of the gradient and Hessian approximations as the optimization progresses. Numerical results on two machine learning problems showcase the efficacy and efficiency of the practical method. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms