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arXiv 2023年

作者： Nguyen, Nhat Trung Rogozin, Alexander Metelev, Dmitriy Gasnikov, Alexander Moscow Institute of Physics and Technology Moscow Russia Institute for Information Transportation Problems Moscow Russia Caucasus Mathematic Center Adygh State University Moscow Russia Ivannikov Institute for System Programming The Russian Academy of Sciences Research Center for Trusted Artificial Intelligence Moscow Russia

Distributed optimization is an important direction of research in modern optimization theory. Its applications include large scale machine learning, distributed signal processing and many others. The paper studies decentralized min-max optimization for saddle point problems. Saddle point problems arise in training adversarial networks and in robust machine learning. The focus of the work is optimization over (slowly) time-varying networks. The topology of the network changes from time to time, and the velocity of changes is limited. We show that, analogically to decentralized optimization, it is sufficient to change only two edges per iteration in order to slow down convergence to the arbitrary time-varying case. At the same time, we investigate several classes of time-varying graphs for which the communication complexity can be reduced. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

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Symbolic Security Predicates: Hunt Program Weaknesses

Symbolic Security Predicates: Hunt Program Weaknesses

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Ivannikov ISPRAS Open Conference (ISPRAS)

作者： Alexey Vishnyakov Vlada Logunova Eli Kobrin Daniil Kuts Darya Parygina Andrey Fedotov Ivannikov Institute for System Programming of the RAS Moscow Institute of Physics and Technology Moscow Russia Lomonosov Moscow State University

ISBN: (纸本)9781665423311

Dynamic symbolic execution (DSE) is a powerful method for path exploration during hybrid fuzzing and automatic bug detection. We propose security predicates to effectively detect undefined behavior and memory access violation errors. Initially, we symbolically execute program on paths that don't trigger any errors (hybrid fuzzing may explore these paths). Then we construct a symbolic security predicate to verify some error condition. Thus, we may change the program data flow to entail null pointer dereference, division by zero, out-of-bounds access, or integer overflow weaknesses. Unlike static analysis, dynamic symbolic execution does not only report errors but also generates new input data to reproduce them. Furthermore, we introduce function semantics modeling for common C/C++ standard library functions. We aim to model the control flow inside a function with a single symbolic formula. This assists bug detection, speeds up path exploration, and overcomes overconstraints in path predicate. We implement the proposed techniques in our dynamic symbolic execution tool Sydr. Thus, we utilize powerful methods from Sydr such as path predicate slicing that eliminates irrelevant constraints. We present Juliet Dynamic to measure dynamic bug detection tools accuracy. The testing system also verifies that generated inputs trigger sanitizers. We evaluate Sydr accuracy for 11 CWEs from Juliet test suite. Sydr shows 95.59% overall accuracy. We make Sydr evaluation artifacts publicly available to facilitate results reproducibility.

关键词： Computer bugs Semantics Static analysis Fuzzing Libraries Reproducibility of results Security

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Location–allocation problem for green efficient two-stage vehicle-based logistics system: A type-2 neutrosophic multi-objective modeling approach

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Expert Systems with Applications 2024年 238卷

作者： Das, Soumen Kumar Yu, Vincent F. Roy, Sankar Kumar Weber, Gerhard Wilhelm Department of Pure and Applied Sciences Midnapore City College Kuturia West Bengal Bhadutala721129 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India Department of Industrial Management National Taiwan University of Science and Technology Taipei Taiwan Center for Cyber-Physical System Innovation National Taiwan University of Science and Technology Taipei Taiwan Faculty of Engineering Management Poznan University of Technology Poznan Poland IAM METU Ankara Turkey

In recent decades, global climate change has become one of the most critical environmental issues, leading to increased environmental and social concerns about the sustainability of logistics networks. This study proposes a novel multi-objective, multi-facility location–allocation model for a two-stage solid logistics network that supports green practices. To account for uncertainty in real-world problems, some parameters of the model are represented as triangular type-2 neutrosophic numbers to deal with hesitant situations. The fuzzy model is then converted into a deterministic one using a new ranking approach. Three conflicting objective functions – minimizing total financial costs, maximizing customers’ satisfaction levels, and ensuring sustainable and effective conveyances – are simultaneously optimized using the ϵ-constraint approach. The proposed model and solution approach are tested with two numerical examples. A comparative study is also presented, comparing the proposed approach with other Pareto-based multi-objective approaches, such as the global criterion approach, multi-objective fuzzy programming, and weighted Chebychev programming. Finally, the paper concludes with some remarks. © 2023

关键词： Sustainable development

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High-Probability Convergence for Composite and Distributed Stochastic Minimization and Variational Inequalities with Heavy-Tailed Noise

arXiv

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arXiv 2023年

作者： Gorbunov, Eduard Sadiev, Abdurakhmon Danilova, Marina Horváth, Samuel Gidel, Gauthier Dvurechensky, Pavel Gasnikov, Alexander Richtárik, Peter Mohamed bin Zayed University of Artificial Intelligence United Arab Emirates King Abdullah University of Science and Technology Saudi Arabia Moscow Institute of Physics and Technology Russia Université de Montréal and Mila Canada Canada CIFAR AI Canada Weierstrass Institute for Applied Analysis and Stochastics Germany University Innopolis Russia Ivannikov Institute for System Programming RAS Russia Skolkovo Institute of Science and Technology Russia

High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented naïvely, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. In addition, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

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Verifying cryptographic protocols by Tamarin Prover

Verifying cryptographic protocols by Tamarin Prover

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2020 Ivannikov Memorial Workshop, IVMEM 2020

作者： Vinarskii, Evgenii Demakov, Alexey Kamkin, Alexander Yevtushenko, Nina Moscow Institute of Physics and Technology Higher School of Economics Ivannikov Institute for System Programming of the Ras Lomonosov Moscow State University Moscow Russia

ISBN: (纸本)9781728190884

Cryptographic protocols are utilized for establishing a secure session between 'honest' agents which communicate strictly according to the protocol rules as well as for ensuring the authenticated and confidential transmission of messages. The specification of a cryptographic protocol is usually presented as a set of requirements for the sequences of transmitted messages including the format of such messages. Note that protocol can describe several execution scenarios. All these requirements lead to a huge formal specification for a real cryptographic protocol and therefore, it is difficult to verify the security of the whole cryptographic protocol at once. In this paper, to overcome this problem, we suggest verifying the protocol security for its fragments. Namely, we verify the security properties for a special set of so-called traces of the cryptographic protocol. Intuitively, a trace of the cryptographic protocol is a sequence of computations, value checks, and transmissions on the sides of 'honest' agents permitted by the protocol. In order to choose such set of traces, we introduce an Adversary model and the notion of a similarity relation for traces. We then verify the security properties of selected traces with Tamarin Prover. Experimental results for the EAP and Noise protocols clearly show that this approach can be promising for automatic verification of large protocols. © 2020 IEEE.

关键词： Cryptography

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The first optimal algorithm for smooth and strongly-convex-strongly-concave minimax optimization 22

The first optimal algorithm for smooth and strongly-convex-s...

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Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Dmitry Kovalev Alexander Gasnikov King Abdullah University of Science and Technology Thuwal Saudi Arabia Moscow Institute of Physics and Technology Dolgoprudny Russia and Institute for System Programming RAS Research Center for Trusted Artificial Intelligence Moscow Russia and National Research University Higher School of Economics Moscow Russia

ISBN: (纸本)9781713871088

In this paper, we revisit the smooth and strongly-convex-strongly-concave minimax optimization problem. Zhang et al. (2021) and Ibrahim et al. (2020) established the lower bound $\Omega\left(\sqrt{\kappa_x\kappa_y} \log \frac{1}{\epsilon}\right)$ on the number of gradient evaluations required to find an ε-accurate solution, where kx and ky are condition numbers for the strong convexity and strong concavity assumptions. However, the existing state-of-the-art methods do not match this lower bound: algorithms of Lin et al. (2020) and Wang and Li (2020) have gradient evaluation complexity $\mathcal{O}\left(\sqrt{\kappa_x\kappa_y} \log^3 \frac{1}{\epsilon}\right)$ and $\mathcal{O}\left( \sqrt{\kappa_x\kappa_y}\log^3 (\kappa_x\kappa_y)\log\frac{1}{\epsilon}\right)$, respectively. We fix this fundamental issue by providing the first algorithm with O (√kxky log 1/ε) gradient evaluation complexity. We design our algorithm in three steps: (i) we reformulate the original problem as a minimization problem via the pointwise conjugate function; (ii) we apply a specific variant of the proximal point algorithm to the reformulated problem; (iii) we compute the proximal operator inexactly using the optimal algorithm for operator norm reduction in monotone inclusions.

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Accelerated primal-dual gradient method for smooth and convex-concave saddle-point problems with bilinear coupling 22

Accelerated primal-dual gradient method for smooth and conve...

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Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Dmitry Kovalev Alexander Gasnikov Peter Richtárik King Abdullah University of Science and Technology Thuwal Saudi Arabia Moscow Institute of Physics and Technology Dolgoprudny Russia and Institute for System Programming RAS Research Center for Trusted Artificial Intelligence Moscow Russia and National Research University Higher School of Economics Moscow Russia

ISBN: (纸本)9781713871088

In this paper we study the convex-concave saddle-point problem minx maxy f(x) + yTAx – g(y), where f(x) and g(y) are smooth and convex functions. We propose an Accelerated Primal-Dual Gradient Method (APDG) for solving this problem, achieving (i) an optimal linear convergence rate in the strongly-convex-strongly-concave regime, matching the lower complexity bound (Zhang et al., 2021), and (ii) an accelerated linear convergence rate in the case when only one of the functions f(x) and g(y) is strongly convex or even none of them are. Finally, we obtain a linearly convergent algorithm for the general smooth and convex-concave saddle point problem minx maxy F(x, y) without the requirement of strong convexity or strong concavity.

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Effective rectification of terahertz electromagnetic fields in a ferrimagnetic iron garnet

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Physical Review B 2023年第9期108卷 094439-094439页

作者： T. G. H. Blank E. A. Mashkovich K. A. Grishunin C. F. Schippers M. V. Logunov B. Koopmans A. K. Zvezdin A. V. Kimel Radboud University Institute for Molecules and Materials 6525 AJ Nijmegen Netherlands Department of Applied Physics Eindhoven University of Technology P.O. Box 513 Eindhoven 5600 MB Netherlands Institute of Physics II University of Cologne D-50937 Cologne Germany Kotel'nikov Institute of Radioengineering and Electronics 125009 Moscow Russia Prokhorov General Physics Institute of the Russian Academy of Sciences 119991 Moscow Russia Institute of Advanced Technology and Industrial Programming MIREA Russian Technological University 119454 Moscow Russia

It is found that single-cycle THz electromagnetic fields efficiently excite a GHz spin resonance mode in ferrimagnetic Tm3Fe5O12, despite the near absence of GHz spectral components in the exciting THz pulse. By analyzing how the efficiency of excitation depends on the orientation and strength of the THz electric field, we show that it can be explained in terms of the nonlinear THz inverse Cotton-Mouton effect. Here, the THz electric field gets effectively rectified and acts on the ferrimagnetic spins as a unipolar effective magnetic field pulse. This interpretation is confirmed by a theoretical model based on the phenomenological analysis of the effective magnetic field, combined with the equations of motion derived from the effective Lagrangian for a ferrimagnet. Moreover, by using the outcome of two-dimensional THz spectroscopy, we conjecture a quantum-mechanical interpretation of the observed effect in terms of impulsive stimulated Raman scattering of THz photons by the crystal-field split f−f electronic transitions of Tm3+.

关键词： Faraday effect Magnetism Magneto-optical effect Magneto-optics Nonlinear optics Ultrafast magnetization dynamics Ferrimagnets Magnetic insulators Ferromagnetic resonance Terahertz spectroscopy Ultrafast pump-probe spectroscopy

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Evaluating carbon cap and trade policy effects on a multi-period bi-objective closed-loop supply chain in retail management under mixed uncertainty: Towards greener horizons

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Expert Systems with Applications 2024年 250卷

作者： Bhunia, Satyajit Das, Soumen Kumar Jablonsky, Josef Roy, Sankar Kumar Department of Pure and Applied Science Midnapore City College Kuturia West Bengal Bhadutala721129 India Department of Industrial Management National Taiwan University of Science and Technology Taipei Taiwan Department of Econometrics Faculty of Informatics and Statistics Prague University of Economics and Business Praha 3 Prague Czech Republic Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India

In response to the growing imperative of addressing environmental concerns and aligning with governmental regulations in supply chain management, this study navigates the optimization landscape of closed-loop supply chains through the lens of carbon cap and trade policy. The optimization model aims to account for the impact of consumer demands, distribution networks, and retail operations on the overall closed-loop supply chain dynamics. The innovative approach introduces an optimization model designed to grapple with the challenges posed by imprecise information within an intuitionistic type-2 fuzzy framework. The bi-objective mixed-integer model integrates pivotal objectives, including carbon emissions reduction, total cost minimization, and trade policy compliance. For a nuanced comprehension of the proposed model, we present three numerical examples, offering clarity on its complexities. Following this, a sensitivity analysis visually depicts the impact of fluctuations in demand and capacity on the defined objective functions. Furthermore, these conclusions unveil promising avenues for future research and exploration within the ambit of this study. © 2024 Elsevier Ltd

关键词： Multiobjective optimization

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Quantum channels, complex Stiefel manifolds, and optimization

arXiv

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arXiv 2024年

作者： Russkikh, Ivan Volkov, Boris Pechen, Alexander Department of Mathematical Methods for Quantum Technologies Steklov Mathematical Institute of Russian Academy of Sciences 8 Gubkina Str. Moscow119991 Russia University of Science and Technology MISIS 4 Leninsky Prosp. Moscow119049 Russia Ivannikov Institute for System Programming The Russian Academy of Sciences Alexandra Solzhenitsyna str. 25 Moscow109004 Russia

Most general dynamics of an open quantum system is commonly represented by a quantum channel, which is a completely positive trace-preserving map (CPTP or Kraus map). Well-known are the representations of quantum channels by Choi matrices and by Kraus operator-sum representation (OSR). As was shown before, one can use Kraus OSR to parameterize quantum channels by points of a suitable quotient under the action of the unitary group of some complex Stiefel manifold. In this work, we establish a continuity relation (homeomorphism) between the topological space of quantum channels and the quotient of the complex Stiefel manifold. Then the metric on the set of quantum channels induced by the Riemannian metric on the Stiefel manifold is defined. The established relation can be applied to various quantum optimization problems. As an example, we apply it to the analysis of extrema points for a wide variety of quantum control objective functionals defined on the complex Stiefel manifolds, including mean value, generation of quantum gates, thermodynamic quantities involving entropy, *** Codes 81Q93 Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum channel

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