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Constrained Continuous-Time Dynamics for Linear Model Predictive Control

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IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 3098-3103页

作者： Adegbege, Ambrose A. Coll New Jersey Dept Elect & Comp Engn Ewing NJ 08628 USA

In this letter, we consider the use of a continuous-time dynamic feedback controller for linear model predictive control (MPC). The controller incorporates both integral-action and anti-windup conditioning and ensures optimality through online emulation of the solution trajectory of an underlying MPC problem. We establish closed-loop stability when the controller is interconnected with an open-loop stable linear-time invariant system using the passivity argument and the invariance principle. We include a computational example to illustrate the effectiveness and the constraint handling capability of the proposed controller.

关键词： Asymptotic stability Power system dynamics Trajectory Stability criteria optimization Steady-state Predictive models Constrained control model predictive control stability of nonlinear systems optimization algorithms

On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial optimization

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arXiv 2024年

作者： Figueira, José Rui Klamroth, Kathrin Stiglmayr, Michael Santos, Julia Sudhoff CEGIST Instituto Superior Técnico Universidade de Lisboa Portugal University of Wuppertal School of Mathematics and Natural Sciences Germany

Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO problems that are actually easy, i.e., solvable in polynomial time. More precisely, we show that MUCO problems with up to two ordinal objective functions plus one real-valued objective function are tractable, and that their complete nondominated set can be computed in polynomial time. For MUCO problems with one ordinal and a second ordinal or real-valued objective function we present an even more efficient algorithm that applies a greedy strategy multiple times. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

SCALABLE DISTRIBUTED optimization OF MULTI-DIMENSIONAL FUNCTIONS DESPITE BYZANTINE ADVERSARIES

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arXiv 2024年

作者： Kuwaranancharoen, Kananart Xin, Lei Sundaram, Shreyas Intel Labs Intel Corporation HillsboroOR97124 United States Department of Computer Science and Engineering The Chinese University of Hong Kong Ma Liu Shui Hong Kong School of Electrical and Computer Engineering Purdue University West LafayetteIN47907 United States

The problem of distributed optimization requires a group of networked agents to compute a parameter that minimizes the average of their local cost functions. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to "Byzantine" agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or assume certain statistical properties of the functions at the agents. In this paper, we provide two resilient, scalable, distributed optimization algorithms for multi-dimensional functions. Our schemes involve two filters, (1) a distance-based filter and (2) a min-max filter, which each remove neighborhood states that are extreme (defined precisely in our algorithms) at each iteration. We show that these algorithms can mitigate the impact of up to F (unknown) Byzantine agents in the neighborhood of each regular agent. In particular, we show that if the network topology satisfies certain conditions, all of the regular agents’ states are guaranteed to converge to a bounded region that contains the minimizer of the average of the regular agents’ *** Codes 93A16, 90C25, 68M15 © 2024, CC BY.

关键词： optimization algorithms

JACOBIAN DESCENT FOR MULTI-OBJECTIVE optimization

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arXiv 2024年

作者： Quinton, Pierre Rey, Valérian LTHI EPFL Switzerland

Many optimization problems require balancing multiple conflicting objectives. As gradient descent is limited to single-objective optimization, we introduce its direct generalization: Jacobian descent (JD). This algorithm iteratively updates parameters using the Jacobian matrix of a vector-valued objective function, in which each row is the gradient of an individual objective. While several methods to combine gradients already exist in the literature, they are generally hindered when the objectives conflict. In contrast, we propose projecting gradients to fully resolve conflict while ensuring that they preserve an influence proportional to their norm. We prove significantly stronger convergence guarantees with this approach, supported by our empirical results. Our method also enables instance-wise risk minimization (IWRM), a novel learning paradigm in which the loss of each training example is considered a separate objective. Applied to simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. Additionally, we outline an efficient implementation of JD using the Gramian of the Jacobian matrix to reduce time and memory requirements. © 2024, CC BY.

关键词： optimization algorithms

Coherent Local Explanations for Mathematical optimization

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arXiv 2025年

作者： Otto, Daan Kurtz, Jannis Birbil, Ilker Amsterdam Business School University of Amsterdam Amsterdam Netherlands

The surge of explainable artificial intelligence methods seeks to enhance transparency and explainability in machine learning models. At the same time, there is a growing demand for explaining decisions taken through complex algorithms used in mathematical optimization. However, current explanation methods do not take into account the structure of the underlying optimization problem, leading to unreliable outcomes. In response to this need, we introduce Coherent Local Explanations for Mathematical optimization (CLEMO). CLEMO provides explanations for multiple components of optimization models, the objective value and decision variables, which are coherent with the underlying model structure. Our sampling-based procedure can provide explanations for the behavior of exact and heuristic solution algorithms. The effectiveness of CLEMO is illustrated by experiments for the shortest path problem, the knapsack problem, and the vehicle routing problem. © 2025, CC BY.

关键词： optimization algorithms

Practical Portfolio optimization with Metaheuristics: Pre-assignment Constraint and Margin Trading

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arXiv 2025年

作者： Poon, Hang Kin Hong Kong Metropolitan University Hong Kong

Portfolio optimization is a critical area in finance, aiming to maximize returns while minimizing risk. Metaheuristic algorithms were shown to solve complex optimization problems efficiently, with Genetic algorithms and Particle Swarm optimization being among the most popular methods. This paper introduces an innovative approach to portfolio optimization that incorporates pre-assignment to limit the search space for investor preferences and better results. Additionally, taking margin trading strategies in account and using a rare performance ratio to evaluate portfolio efficiency. Through an illustrative example, this paper demonstrates that the metaheuristic-based methodology yields superior risk-adjusted returns compared to traditional benchmarks. The results highlight the potential of metaheuristics with help of assets filtering in enhancing portfolio performance in terms of risk adjusted return. © 2025, CC BY.

关键词： optimization algorithms

optimization on black-box function by parameter-shift rule

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arXiv 2025年

作者： Hai, Vu Tuan Nara Institute of Science and Technology 8916–5 Takayama-cho Nara Ikoma630-0192 Japan

Machine learning has been widely applied in many aspects, but training a machine learning model is increasingly difficult. There are more optimization problems named "black-box" where the relationship between model parameters and outcomes is uncertain or complex to trace. Currently, optimizing black-box models that need a large number of query observations and parameters becomes difficult. To overcome the drawbacks of the existing algorithms, in this study, we propose a zeroth-order method that originally came from quantum computing called the parameter-shift rule, which has used a lesser number of parameters than previous methods. © 2025, CC BY.

关键词： optimization algorithms

ADAPTIVE MOMENT ESTIMATION optimization ALGORITHM USING PROJECTION GRADIENT FOR DEEP LEARNING

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arXiv 2025年

作者： Li, Yongqi Zhang, Xiaowei School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 China

Training deep neural networks is challenging. To accelerate training and enhance performance, we propose PadamP, a novel optimization algorithm. PadamP is derived by applying the adaptive estimation of the p-th power of the second-order moments under scale invariance, enhancing projection adaptability by modifying the projection discrimination condition. It is integrated into Adam-type algorithms, accelerating training, boosting performance, and improving generalization in deep learning. Combining projected gradient benefits with adaptive moment estimation, PadamP tackles unconstrained non-convex problems. Convergence for the non-convex case is analyzed, focusing on the decoupling of β1 and β2. Unlike prior work relying on β1/√β2 Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

An Algorithm to Solve Cardinality Constrained Quadratic optimization Problem with an Application to the Best Subset Selection in Regression

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arXiv 2025年

作者： Singh, Vikram Sun, Min University of Central Oklahoma EdmondOK United States The University of Alabama TuscaloosaAL United States

A lot of problems, from fields like sparse signal processing, statistics, portfolio selection, and machine learning, can be formulated as a cardinality constraint optimization problem. The cardinality constraint gives the problem a discrete nature, making it computationally challenging to solve as the dimension of the problem increases. In this work, we present an algorithm to solve the cardinality constraint quadratic optimization problem using the framework of the interval branch-and-bound. Interval branch-and-bound is a popular approach for finding a globally optimal solution in the field of global optimization. The proposed method is capable of solving problems of a wide range of dimensions. In particular, we solve the classical best subset selection problem in regression and compare our algorithm against another branch-and-bound method and GUROBI’s quadratic mixed integer solver. Numerical results show that the proposed algorithm outperforms the first and is competitive with the second solver. Keywords— Quadratic optimization, Cardinality constraint, Interval branch-and-bound, Best subset selection, Global optimizationMSC Codes 90C26, 90C57, 65K05 © 2025, CC BY.

关键词： optimization algorithms