Min-max Optimization Problem Research Articles

Estimating Asset Pricing Models in the Presence of Cross-Sectionally Correlated Pricing Errors

In this study, we propose an adversarial learning approach to the asset pricing model estimation problem which aims to find estimates of factors and loadings that capture time-series covariations while minimizing the worst-case cross-sectional pricing errors. The proposed estimator is defined by a novel min-max optimization problem in which finding a solution is known to be difficult. This contrasts with other related estimators that admit a well-defined analytic solution but do not effectively account for correlations among the pricing errors. To this end, we propose an approximate algorithm based on the alternating optimization procedure and empirically demonstrate that our proposed adversarial estimation framework outperforms other existing factor models, especially when the explanatory power of the pricing model is limited.

Method for prediction magnetic silencing of uncertain energy-saturated extended technical objects in prolate spheroidal coordinate system

Aim. Development of method for prediction by energy-saturated extended technical objects magnetic silencing based on magnetostatics geometric inverse problems solution and magnetic field spatial spheroidal harmonics calculated in prolate spheroidal coordinate system taking into account of technical objects magnetic characteristics uncertainties. Methodology. Spatial prolate spheroidal harmonics of extended technical objects magnetic field model calculated as magnetostatics geometric inverse problems solution in the form of nonlinear minimax optimization problem based on near field measurements for prediction far extended technical objects magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field COMSOL Multiphysics software package used. Nonlinear minimax optimization problems solutions calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction extended technical objects far magnetic field magnitude based on extended technical objects spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system using near field measurements with consideration of extended technical objects magnetic characteristics uncertainty. Originality. The method for prediction by extended technical objects magnetic cleanliness based on spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of magnetic characteristics uncertainty is developed. Practical value. The important practical problem of prediction extended technical objects magnetic silencing based on the spatial prolate spheroidal harmonics of the magnetic field model in the prolate spheroidal coordinate system with consideration of extended technical objects magnetic characteristics uncertainty solved. References 48, figures 2.

A Quasi-Newton Subspace Trust Region Algorithm for Nonmonotone Variational Inequalities in Adversarial Learning over Box Constraints

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In this paper, we propose a quasi-Newton subspace trust region (QNSTR) algorithm for the least squares problems defined by the smoothing approximation of nonsmooth equations. Based on the structure of the nonmonotone VI, we use an adaptive quasi-Newton formula to approximate the Hessian matrix and solve a low-dimensional strongly convex quadratic program with ellipse constraints in a subspace at each step of the QNSTR algorithm efficiently. We prove the global convergence of the QNSTR algorithm to an ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document}-first-order stationary point of the min-max optimization problem. Moreover, we present numerical results based on the QNSTR algorithm with different subspaces for a mixed generative adversarial networks in eye image segmentation using real data to show the efficiency and effectiveness of the QNSTR algorithm for solving large-scale min-max optimization problems.

Optimality Conditions and Numerical Algorithms for a Class of Linearly Constrained Minimax Optimization Problems

Optimality Conditions and Numerical Algorithms for a Class of Linearly Constrained Minimax Optimization Problems

Mobility-aware parallel offloading and resource allocation scheme for vehicular edge computing

Vehicle edge computing (VEC) enhances the distributed task processing capability within intelligent vehicle-infrastructure cooperative systems (i-VICS) by deploying servers at the network edge. However, the proliferation of onboard sensors and the continual emergence of new applications have exacerbated the inadequacy of wireless spectrum resources and edge server resources, while the high mobility of vehicles reduces reliability in task processing, resulting in increased communication and task processing delays. To address these challenges, we propose a mobile-aware Many-to-Many Parallel (MTMP) offloading scheme that integrates: a) millimeter-wave (mmWave) and cellular vehicle-to-everything (C-V2X) to mitigate excessive communication delays; and b) leveraging the underutilized resources of surrounding vehicles and parallel offloading to mitigate excessive task processing delays. To minimize the average completion delay of all tasks, this paper formulates the objective as a min-max optimization problem and solves it using the maximum entropy method (MEM), the Lagrange multiplier method, and an iterative algorithm. Extensive experimental results demonstrate the superior performance of the proposed scheme in comparison with other baseline algorithms. Specifically, our proposal achieves a 47 % reduction in task completion delay under optimal conditions, a 31.3 % increase in task completion rate, and a 30 % decrease in program runtime compared to the worst-performing algorithm.

A two-timescale neurodynamic approach to robust distributed model predictive control for nonlinear systems

In this paper, a robust distributed model predictive control strategy is proposed for nonlinear dynamical systems affected by bounded disturbances. Grounded on sequential quadratic programming, a two-timescale recurrent neural network paradigm is deployed for solving minimax optimization problems. Sufficient criteria for the two-timescale recurrent neural network are delineated, which specifically guarantee its stability and optimality. Under these conditions, it is demonstrated that the recurrent neural network converges to optimal solutions, thereby enhancing the robustness of the control strategy. The simulation results exhibit significantly enhanced convergence in comparison to the mono-timescale recurrent neural network.

The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions

The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.

Tri-composed fuzzy relation inequality with weighted-max-min composition and the relevant min-max optimization problem

In the existing works, the classical fuzzy relation inequality (FRI) with double-composed operators has been introduced to describe the P2P network system. In this work, considering the successful rate of the line connection within the P2P network system, we establish the so-called tri-composed FRI, with a weighted-max-min composition, for the first time. We study the solutions induced through paths and further construct the complete solution set of the tri-composed FRI using the path-induced solutions. Moreover, the whole solution set could be fully determined by all the path-induced solutions and its unique maximum solution. Furthermore, considering a specific optimal management objective in the P2P network, we further study the min-max optimization problem with the tri-composed FRI constraints. A path-based algorithm is proposed for handling the problem we studied, accompanied by an illustrative example.

A convex cone programming based implicit material point method

For conventional Material Point Method (MPM), both explicit-based and implicit-based MPM have shortcomings: explicit MPM has high requirements on time steps, and implicit MPM has high requirements on convergence. To circumvent these limitations, this paper innovatively proposes a convex cone programming-based implicit MPM (CP-MPM) algorithm, which ensures excellent convergence of solving complex problems involving large deformation, regardless of the chosen time step. In the proposed CP-MPM, the governing equations are initially transformed into a stationary point of a multivariable functional, leveraging the generalized Hellinger-Reissner (HR) variational principle. This stationary point problem is subsequently reformulated as a min-max convex cone optimization problem, with constraints originating from elastoplastic constitutive equations. In addition, a novel particle-based adhesive-frictional contact algorithm is proposed to effectively tackle the interaction between MPM domain and rigid bodies. The contact inequality between material points and rigid bodies is transformed into convex cone constraints, which rigorously prevent material point penetration and facilitate the imposition of irregular boundary conditions. Both elastic and elastoplastic problems involving contact under static or dynamic loading are ultimately represented as standard second-order cone programming (SOCP) problems, which is effectively solved by employing the Primal-Dual Interior Point (PDIP) method. The robustness, accuracy and convergence of the proposed method are validated through a series of elastic and elastoplastic benchmark problems. All results demonstrate the CP-MPM is a very promising method for implicitly solving complex practices.

Boosting generalization of fine-tuning BERT for fake news detection

Using deep neural networks to detect fake news has gradually become an extremely important field of research. Recent studies, which adopt fine-tuning BERT to detect fake news, have yielded promising results. Unfortunately, fine-tuning BERT is prone to overfitting the training data, which may reduce its generalization ability. The problem remains challenging when one tries to generalize the detector to unseen fake news. First, we investigate the effects of several fine-tuning strategies on the generalization of BERT models used in fake news detection. Specifically, we explore three fine-tuning strategies, which include initialization of model parameters, freezing of model parameters, and training iterations for fine-tuning. Besides, we propose an adversarial fine-tuning strategy to boost the generalization of fine-tuning BERT for fake news detection. In detail, we define the BERT fine-tuning procedure as a mini-max optimization problem. We also propose a novel adversarial fine-tuning training strategy based on feature regularization, called FGM-FRAT, to further improve the generalization. Specifically, we propose to adopt the model representation to guide the generation of adversarial examples during adversarial training on the word vector space. The proposed method outperforms state-of-the-art fake news detection methods. Extensive experiments on several benchmark databases, which include FakeNewsNet, BuzzFeedNews, LIAR, WELFake, and KaggleFakeNews, show that using the proposed method improves the generalization accuracy from 61% to 73% for BERT. It indicates that our FGM-FRAT can greatly improve the generalization of fine-tuning BERT for fake news detection. Moreover, the proposed method also can be extended to other pre-trained language models and other text classification tasks.

Solving Maxmin Optimization Problems via Population Games

Population games are games with a finite set of available strategies and an infinite number of players, in which the reward for choosing a given strategy is a function of the distribution of players over strategies. The paper shows that, in a certain class of maxmin optimization problems, it is possible to associate a population game to a given maxmin problem in such a way that solutions to the optimization problem are found from Nash equilibria of the associated game. Iterative solution methods for maxmin optimization problems can then be derived from systems of differential equations whose trajectories are known to converge to Nash equilibria. In particular, we use a discrete-time version of the celebrated replicator equation of evolutionary game theory, also known in machine learning as the exponential multiplicative weights algorithm. The resulting algorithm can be viewed as a generalization of the Iteratively Reweighted Least Squares (IRLS) method, which is well known in numerical analysis as a useful technique for solving Chebyshev function approximation problems on a finite grid. Examples are provided to show the use of the generalized IRLS method in collective investment and in decision making under model uncertainty.

A stable implicit nodal integration-based particle finite element method (N-PFEM) for modelling saturated soil dynamics

In this study, we present a novel nodal integration-based particle finite element method (N-PFEM) designed for the dynamic analysis of saturated soils. Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner (HR) variational principle, creating an implicit PFEM formulation. To mitigate the volumetric locking issue in low-order elements, we employ a node-based strain smoothing technique. By discretising field variables at the centre of smoothing cells, we achieve nodal integration over cells, eliminating the need for sophisticated mapping operations after re-meshing in the PFEM. We express the discretised governing equations as a min-max optimisation problem, which is further reformulated as a standard second-order cone programming (SOCP) problem. Stresses, pore water pressure, and displacements are simultaneously determined using the advanced primal-dual interior point method. Consequently, our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation. Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy, obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches. This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

ATZSL: Defensive Zero-Shot Recognition in the Presence of Adversaries

Zero-shot learning (ZSL) has received extensive attention recently especially in areas of fine-grained object recognition, retrieval, and image captioning. Due to the complete lack of training samples and high requirement of defense transferability, the ZSL model learned is particularly vulnerable against adversarial attacks. Recent work also showed adversarially robust generalization requires more data. This may significantly affect the robustness of ZSL. However, very few efforts have been devoted towards this direction. In this paper, we take an initial attempt, and propose a generic formulation to provide a systematical solution (named ATZSL) for learning a defensive ZSL model. It is capable of achieving better generalization on various adversarial objects recognition while only losing a negligible performance on clean images for unseen classes, by casting ZSL into a min-max optimization problem. To address it, we design a defensive relation prediction network, which can bridge the seen and unseen class domains via attributes to generalize prediction and defense strategy. Additionally, our framework can be extended to deal with the poisoned scenario of unseen class attributes. An extensive group of experiments are then presented, demonstrating that ATZSL obtains remarkably more favorable trade-off between model transferability and robustness, over currently available alternatives under various settings.

Adversarial Information Bottleneck.

The information bottleneck (IB) principle has been adopted to explain deep learning in terms of information compression and prediction, which are balanced by a tradeoff hyperparameter. How to optimize the IB principle for better robustness and figure out the effects of compression through the tradeoff hyperparameter are two challenging problems. Previous methods attempted to optimize the IB principle by introducing random noise into learning the representation and achieved the state-of-the-art performance in the nuisance information compression and semantic information extraction. However, their performance on resisting adversarial perturbations is far less impressive. To this end, we propose an adversarial IB (AIB) method without any explicit assumptions about the underlying distribution of the representations, which can be optimized effectively by solving a min-max optimization problem. Numerical experiments on synthetic and real-world datasets demonstrate its effectiveness on learning more invariant representations and mitigating adversarial perturbations compared to several competing IB methods. In addition, we analyze the adversarial robustness of diverse IB methods contrasting with their IB curves and reveal that IB models with the hyperparameter β corresponding to the knee point in the IB curve achieve the best tradeoff between compression and prediction and has the best robustness against various attacks.

Method for prediction and control by uncertain microsatellite magnetic cleanliness based on calculation and compensation magnetic field spatial harmonics

Aim. Development of method for prediction and control the microsatellite magnetic cleanliness taking into account the uncertainties of the magnetic characteristics of the microsatellite, based on calculation the magnetic field spatial spherical harmonics in the area of the onboard magnetometer installation and using compensating multipoles. Methodology. Spatial spherical harmonics of microsatellite magnetic field in the area of the onboard magnetometer installation calculated as solution of nonlinear minimax optimization problem based on near field measurements for prediction far spacecraft magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field. Values of the compensating dipoles, quadrupoles and octupoles and coordinates of them placement inside the spaceship for compensation of the dipoles, quadrupoles and octupoles components of the microsatellite initial magnetic field also calculated as solution of nonlinear minimax optimization problem. Both solutions of this nonlinear minimax optimization problems calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction spacecraft far magnetic field magnitude based on spacecraft spatial spherical harmonics of the magnetic field using near field measurements and compensation of the dipoles, quadrupoles and octupoles components of the initial magnetic field with consideration of spacecraft magnetic characteristics uncertainty for ensuring the microsatellite magnetic cleanliness. Originality. The method for prediction and control by spacecraft magnetic cleanliness based on calculation spatial spherical harmonics of the magnetic field in the area of the onboard magnetometer installation using compensation of the dipoles, quadrupoles and octupoles components of the initial magnetic field with consideration of magnetic characteristics uncertainty is developed. Practical value. The important practical problem of ensuring the magnetic cleanliness of the «Sich-2» microsatellite family based on the spatial spherical harmonics of the magnetic field model using the compensation of the dipole, quadrupole and octupole components of the output magnetic field of the sensor for the kinetic parameters of the neutral component of the space plasma at the point of installation of the on-board magnetometer LEMI-016 by setting the compensating dipole, quadrupole and octupole with consideration of spacecraft magnetic characteristics uncertainty solved.

Path Following Model Predictive Control of a Coupled Autonomous Underwater Vehicle

The operation of an autonomous underwater vehicle (AUV) faces challenges in following predetermined waypoints due to coupled motions under environmental disturbances. To address this, a 3D path following guidance and control system is developed in this work based on the line-of-sight (LOS) guidance method. Conventionally, the 3D path following problem is transformed into heading and depth control problems, assuming that the motion of the vehicle is decoupled in horizontal and depth coordinates. The proposed control system design avoids this simplifying assumption by transforming the problem into a 3D position and orientation tracking problem. This design is achieved by computing a 2D horizontal coordinate based on the desired heading and then computing a corresponding LOS depth coordinate. A model predictive controller (MPC) is then implemented using the 3D LOS coordinate and the computed orientation vector. The MPC obtains a robust control by solving a minimax optimisation problem considering the effects of unknown ocean disturbances. The effectiveness of the proposed guidance and control system is demonstrated through the simulation of a prototype AUV system. Numerical results show that the AUV can follow predetermined waypoints in the presence of time-varying disturbances, and the system is steered at a constant surge speed that is proportional to the radius of the circle of acceptance used to implement the guidance system.

Arithmetic average density fusion - Part I: Some statistic and information-theoretic results

Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the target distribution by the arithmetic average (AA) of a finite number of sub-distributions which constitute a mixture. While the mixture has been widely used for single sensor filter design, it is only recent that the AA fusion demonstrates compelling performance for multi-sensor filter design. In this paper, some statistic and information-theoretic results are given on the covariance consistency, mean square error, mode-preservation capacity, and the information divergence of the AA fusion approach. In particular, based on the concept of conservative fusion, the relationship of the AA fusion with the existing conservative fusion approaches such as covariance union and covariance intersection is exposed. A suboptimal weighting approach has been proposed, which jointly with the best mixture-fit property of the AA fusion leads to a max–min optimization problem. Linear Gaussian models are considered for algorithm illustration and simulation comparison, resulting in the first-ever AA fusion-based multi-sensor Kalman filter. This is the first part of a series of papers that provide a comprehensive and thorough study of the AA fusion methodology and its application for target tracking. Extension and derivation of the AA fusion in the context of random finite set filters are provided in the consequent papers.

Weighted-minimax programming subject to the RTA max-product fuzzy relation inequality system and its optimal strong solution

Recently the max-product fuzzy relation inequalities have been applied to describe the wireless communication basic-station system. In this paper we further define the so-called random-term-absent (RTA) max-product fuzzy relation inequalities, which enable the system to bear a random communication line fault. Moreover, in order to make all basic-stations take part in the communication activity and avoid waste of resources, we investigate the strong solution to the RTA system. In general case, the strong solution set is composed by a unique maximum strong solution and a finite number of minimal strong solutions. Based on the practical application consideration, we propose the corresponding weighted minimax optimization problem. Detailed algorithm is designed for obtaining the optimal strong solution of such an optimization problem, with an illustrative example.

Joint Optimization of Security Strength and Resource Allocation for Computation Offloading in Vehicular Edge Computing

Vehicular Edge Computing (VEC) is a promising new paradigm that has attracted much attention in recent years, which can enhance the storage and computing capabilities of vehicular networks to provide users with low latency and high-quality services. Due to the open access and unreliable wireless channels, some appropriate security measures should be implemented in the VEC to ensure information security. However, the operation of the security mechanism dominates supererogatory computing resources, thus affecting the performance of VEC systems. The scarcity of computation and energy resources of the vehicles conflicts with the requirement of tasks for time delay and information security. In this paper, taking the driving velocity and position of the vehicles, the number of lanes, the model and density of the attackers, and security strength into consideration, we formulate a max-min optimization problem to jointly optimize offloading decision, transmit power, task computation frequency, encryption computation frequency, edge computation frequency, and block length to obtain optimal secure information capacity and local computation delay. The formulated optimization problem is a mixed integer nonlinear programming (MINLP), which is intractable. We apply the generalized benders decomposition (GBD)-based method to solve it. The simulation results show that our proposed algorithms have convergence and effectiveness and achieve fairness among vehicles on the road.

Bi-level multi-objective robust optimization for performance improvements in integrated energy system with solar fuel production

The authors design an integrated energy system with solar fuel preparation as the core, integrating cooling, heating, electricity and fuel cell vehicles, aiming to meet the multiple energy needs of users. Fluctuations associated with renewable energy and energy demand pose a challenge to operational planning of systems. Unfortunately, common models do not take into account the impact of such fluctuations on system operation. To mitigate this challenge, the authors develop a bi-level multi-objective robust optimization model to obtain the optimal resilient dispatch of the system. The above model is transformed into a minimax optimization problem to alleviate the difficulties that solving it directly, and two nested algorithms are employed to maximize the energy conversion efficiency, minimize CO2 emissions and energy cost of the system. The energy, environmental and economic effects of system are compared using a robust optimization model and a deterministic optimization model. The operation performances of system in the bi-level robust optimization model are not all better than the results obtained from the deterministic model, because the robust optimization model considers the volatility of solar, wind, and customer loads during system operation. This research provides a feasible method to ensure the stability of the system.