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Generalized-Hukuhara subgradient and its application in optimization problem with interval-valued functions

SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2022年第2期47卷 1-16页

作者： Ghosh, Debdas Debnath, Amit Kumar Chauhan, Ram Surat Mesiar, Radko Indian Inst Technol BHU Dept Math Sci Varanasi 221005 Uttar Pradesh India Slovak Univ Technol Bratislava Fac Civil Engn Radlinskeho 11 Bratislava 81005 Slovakia Palacky Univ Olomouc Dept Algebra & Geometry Fac Sci 17 Listopadu 12 Olomouc 77146 Czech Republic

In this article, the concepts of gH-subgradient and gH-subdifferential of interval-valued functions are illustrated. Several important characteristics of the gH-subdifferential of a convex interval-valued function, e.g., closeness, boundedness, chain rule, etc. are studied. Alongside, we prove that gH-subdifferential of a gH-differentiable convex interval-valued function contains only the gH-gradient. It is observed that the directional gH-derivative of a convex interval-valued function is the maximum of all the products between gH-subgradients and the direction. Importantly, we prove that a convex interval-valued function is gH-Lipschitz continuous if it has gH-subgradients at each point in its domain. Furthermore, relations between efficient solutions of an optimization problem with interval-valued function and its gH-subgradients are derived.

关键词： convex programming gH-subgradient gH-subdifferential interval optimization problems

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New conditions for finite-time stability of impulsive dynamical systems via piecewise quadratic functions

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IET CONTROL THEORY AND APPLICATIONS 2022年第13期16卷 1341-1351页

作者： Ambrosino, Roberto Ariola, Marco Garone, Emanuele Amato, Francesco Tartaglione, Gaetano Univ Napoli Federico II DIETI Via Claudio I-80125 Naples Italy Univ Napoli Parthenope Ctr Direz Napoli Dipartimento Ingn Isola C4 Naples Italy Univ Libre Bruxelles Dept Control & Syst Theory Ecole Polytech Bruxelles Ave F Roosevelt Brussels Belgium

In this paper, the use of time-varying piecewise quadratic functions is investigated to characterize the finite-time stability of state-dependent impulsive dynamical linear systems. Finite-time stability defines the behavior of a dynamic system over a bounded time interval. More precisely, a system is said to be finite-time stable if, given a set of initial conditions, its state vector does not exit a predefined domain for a certain finite interval of time. This paper presents new sufficient conditions for finite-time stability based on time-varying piecewise quadratic functions. These conditions can be reformulated as a set of Linear Matrix Inequalities that can be efficiently solved through convex optimization solvers. Different numerical analysis are included in order to prove that the presented conditions are able to improve the results presented so far in the literature.

关键词： convex optimization state-dependent impulsive dynamical linear systems linear systems convex programming stability piecewise linear techniques linear matrix inequalities finite-time stability time-varying piecewise quadratic function time-varying systems numerical analysis bounded time interval

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Modeling the α-max capacity of transportation networks: a single-level mathematical programming formulation

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TRANSPORTATION 2022年第4期49卷 1211-1243页

作者： Zang, Zhaoqi Xu, Xiangdong Chen, Anthony Yang, Chao Tongji Univ Key Lab Rd & Traff Engn Minist Educ Shanghai Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Kowloon Hong Kong Peoples R China

Network capacity, defined as the largest sum of origin-destination (O-D) flows that can be accommodated by the network based on link performance function and traffic equilibrium assignment, is a critical indicator of network-wide performance assessment in transportation planning and management. The typical modeling rationale of estimating network capacity is to formulate it as a mathematical programming (MP), and there are two main approaches: single-level MP formulation and bi-level programming (BLP) formulation. Although single-level MP is readily solvable, it treats the transportation network as a physical network without considering level of service (LOS). Albeit BLP explicitly models the capacity and link LOS, solving BLP in large-scale networks is challenging due to its non-convexity. Moreover, the inconsideration of trip LOS makes the existing models difficult to differentiate network capacity under various traffic states and to capture the impact of emerging trip-oriented technologies. Therefore, this paper proposes the alpha-max capacity model to estimate the maximum network capacity under trip or O-D LOS requirement alpha. The proposed model improves the existing models on three aspects: (a) it considers trip LOS, which can flexibly estimate the network capacity ranging from zero to the physical capacity including reserve, practical and ultimate capacities;(b) trip LOS can intuitively reflect users' maximum acceptable O-D travel time or planners' requirement of O-D travel time;and (c) it is a convex and tractable single-level MP. For practical use, we develop a modified gradient projection solution algorithm with soft constraint technique, and provide methods to obtain discrete trip LOS and network capacity under representative traffic states. Numerical examples are presented to demonstrate the features of the proposed model as well as the solution algorithm.

关键词： Network capacity Trip level of service Flexibility convex programming Gradient projection

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convex Formulation for Optimal Active and Reactive Power Dispatch

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IEEE LATIN AMERICA TRANSACTIONS 2022年第5期20卷 787-798页

作者： da Silva, Mauro Viegas Home-Ortiz, Juan M. Pourakbari-Kasmaei, Mandi Sanches, Jose Roberto Univ Estado Mato Grosso UNEMAT Dept Math Caceres MT Brazil Sao Paulo State Univ Dept Elect Engn Power Syst Planning Lab UNESP Ilha Solteira SP Brazil Aalto Univ Dept Elect Engn & Automat Maarintie 8 Espoo 02150 Finland

This paper proposes a convex programming model to solve the optimal power flow problem (OPF) related to the problems of generation active power dispatch and opportunity costs to meet the reactive power needs in energy markets. The problem is initially represented as a bilevel optimization problem where the upper level considers the minimization of opportunity costs of generating units through a second-order cone programming OPF model, and the lower level is a linear programming model that minimizes the value of active power offered by generators to the market energy. Subsequently, through the concept of strong duality, the problem is transformed into a one-level convex optimization model. Comparisons of the proposed modeling with other level formulations are presented. Results are presented for the IEEE14 and IEEE30 bus systems.

关键词： programming Costs Reactive power Optimization Load flow Jacobian matrices IEEE transactions Bilevel optimization convex programming opportunity costs optimal power flow strong duality

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Objective Frequentist Uncertainty Quantification for Atmospheric CO2 Retrievals

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SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION 2022年第3期10卷 827-859页

作者： Patil, Pratik Kuusela, Mikael Hobbs, Jonathan Carnegie Mellon Univ Dept Stat & Data Sci Pittsburgh PA 15213 USA Carnegie Mellon Univ Machine Learning Dept Pittsburgh PA 15213 USA CALTECH Jet Prop Lab Pasadena CA 91109 USA

The steadily increasing amount of atmospheric carbon dioxide (CO2) is affecting the global climate system and threatening the long-term sustainability of Earth's ecosystem. In order to better understand the sources and sinks of CO2, NASA operates the Orbiting Carbon Observatory-2 and -3 satellites to monitor CO2 from space. These satellites make passive radiance measurements of the sunlight reflected off the Earth's surface in different spectral bands, which are then inverted in an ill-posed inverse problem to obtain estimates of the atmospheric CO2 concentration. In this work, we propose a new CO2 retrieval method that uses known physical constraints on the state variables and direct inversion of the target functional of interest to construct well-calibrated frequentist confidence intervals based on convex programming. We compare the method with the current operational retrieval procedure, which uses prior knowledge in the form of probability distributions to regularize the problem. We demonstrate that the proposed intervals consistently achieve the desired frequentist coverage, while the operational uncertainties are poorly calibrated in a frequentist sense both at individual locations and over a spatial region in a realistic simulation experiment. We also study the influence of specific nuisance state variables on the length of the proposed intervals and identify certain key variables that can greatly reduce the final uncertainty given additional deterministic or probabilistic constraints. We then develop a principled framework to incorporate such additional information into our method.

关键词： Orbiting Carbon Observatory-2 and-3 remote sensing constrained inverse problem frequentist coverage variable importance convex programming

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An efficient partial parallel method with scaling step size strategy for three-block convex optimization problems

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2022年第3期96卷 383-419页

作者： Jiang, Yaning Han, Deren Cai, Xingju Nanjing Univ Dept Math Nanjing 210093 Peoples R China Beihang Univ Sch Math Sci LMIB Beijing 100191 Peoples R China Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210093 Peoples R China

A popular optimization model arising from image processing is the separable optimization problem whose objective function is the sum of three independent functions, and the variables are coupled by a linear equality. In this paper, we propose to solve such problem by a new partially parallel splitting method, whose step sizes for the primal and the dual variables in correction step are not necessarily identical. We establish the global convergence, and study the convergence rate on this varying ADMM-based prediction-correction method named as VAPCM. We derive the worst-case O(1/t) convergence rate in both the ergodic and non-ergodic senses. We also show that the convergence rate can be improved to o(1/t). Moreover, under the error bound assumptions, we establish the global linear convergence of VAPCM. We apply the new method to solve problems in robust principal component analysis and image decomposition. Numerical results indicate that the new method is efficient.

关键词： convex programming Alternating direction method of multipliers Partially parallel splitting method Convergence rate

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Joint design of the discrete phase transmit sequence and receive filter in radar systems

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IET RADAR SONAR AND NAVIGATION 2022年第2期16卷 315-326页

作者： Pishrow, Mohammad Mehdi Abouei, Jamshid Yazd Univ Dept Elect Engn POB 9195-741 Yazd Iran

In this study, the joint design of discrete phase transmit sequences and receive filters with the low peak sidelobe level and integrated sidelobe level in radar systems is considered. The problem is formulated as a minimisation of the peak (integrated) sidelobe level, forcing a unimodular discrete phase constraint at the design stage. To deal with the resulting non-convex and in general the NP-hard optimisation problem, an iterative method based on the alternate optimisation approach is proposed. Each iteration of the proposed method involves a non-convex min-max problem to be solved. In addition, a sequential rank-one constraint relaxation framework is proposed to initialise the procedure, each iteration of which requires the solution of a convex problem. Simulation results show that using the proposed framework for jointly finding transmit sequences and receive filters leads to a better peak sidelobe ratio and integrated sidelobe ratio for discrete phase sequences than the optimal mismatched filters design approach.

关键词： iteration methods radar systems matched filters integrated sidelobe ratio convex programming minimisation iterative methods resulting nonconvex low peak sidelobe level radar signal processing integrated sidelobe level optimal mismatched filters design approach NP-hard optimisation problem nonconvex min-max problem minimax techniques signal processing alternate optimisation approach discrete phase transmit sequence convex problem discrete phase sequences jointly finding transmit sequences design stage unimodular discrete phase constraint peak sidelobe ratio

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Robust fuzzy model predictive control for voltage regulation in islanded microgrids

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IET GENERATION TRANSMISSION & DISTRIBUTION 2022年第5期16卷 1013-1029页

作者： Mottaghizadeh, Masood Aminifar, Farrokh Amraee, Turaj Sanaye-Pasand, Majid Univ Tehran Coll Engn Sch Elect & Comp Engn Tehran 113654563 Iran KN Toosi Univ Technol Fac Elect Engn Dept Elect Engn Tehran Iran

An effective robust fuzzy model predictive control (RFMPC) method for secondary voltage control in islanded microgrids (mu Gs) is presented here. In contrast to the existing techniques, which require a detailed model of mu G and an ideal communication network between mu G central controller and primary local controllers, RFMPC is synthesized for a non-linear model of the mu G with various time delays, uncertainties, and bounded disturbances. The famous Takagi-Sugeno fuzzy approach is adopted to approximate the inherently non-linear model of mu G by locally linear dynamics. The Lyapunov-Razumikhin functional method is exploited to deal with time delays. In this regard, sufficient conditions are provided in the form of linear matrix inequalities (LMIs). Then, a sequence of control laws corresponding to a set of terminal constraints is computed offline. Doing so, the online stage is reduced to solving a convex problem with LMI constraints considering the sequence of constraint sets obtained in the offline stage, thereby reducing the computational burden significantly. Robust positive invariance and input-to-state stability property concerning communication network deficiency are then speculated. The effectiveness of the proposed RFMPC is verified via a comprehensive suite of simulations in the MATLAB/SimPowerSystems environment.

关键词： μG central controller delays convex programming voltage control power system stability control laws effective robust fuzzy model predictive control method primary local controllers constraint set sequence input-to-state stability property fuzzy control predictive control linear matrix inequalities time delays islanded microgrids sufficient conditions Lyapunov methods Takagi-Sugeno fuzzy approach robust positive invariance centralised control robust control distributed power generation locally linear dynamics Lyapunov-Razumikhin functional method MATLAB-SimPowerSystems environment LMIs voltage regulation nonlinear model communication network efficiency control law sequences convex problem power generation control secondary voltage control RFMPC method

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Accelerated gradient sliding for structured convex optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2022年第2期82卷 361-394页

作者： Lan, Guanghui Ouyang, Yuyuan Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Clemson Univ Sch Math & Stat Sci Clemson SC 29634 USA

Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding (AGS) method for minimizing the summation of two smooth convex functions with different Lipschitz constants. We show that the AGS method can skip the gradient computation for one of these smooth components without slowing down the overall optimal rate of convergence. This result is much sharper than the classic black-box CP complexity results especially when the difference between the two Lipschitz constants associated with these components is large. We then consider an important class of bilinear saddle point problem whose objective function is given by the summation of a smooth component and a nonsmooth one with a bilinear saddle point structure. Using the aforementioned AGS method for smooth composite optimization and Nesterov's smoothing technique, we show that one only needs O(1/root epsilon) gradient computations for the smooth component while still preserving the optimal O(1/epsilon) overall iteration complexity for solving these saddle point problems. We demonstrate that even more significant savings on gradient computations can be obtained for strongly convex smooth and bilinear saddle point problems.

关键词： convex programming Accelerated gradient sliding Structure Complexity Nesterov's method

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Transmit waveform and receive filter design for multiple-input multiple-output radar with one-bit digital-to-analogue converters

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IET SIGNAL PROCESSING 2022年第7期16卷 873-881页

作者： Wan, Huan Quan, Zhi Liao, Bin Shenzhen Univ Coll Elect & Informat Engn Guangdong Key Lab Intelligent Informat Proc Shenzhen 518060 Peoples R China Shenzhen Polytech Sch Artificial Intelligence Shenzhen Peoples R China

In this paper, we investigate the joint design of transmit waveform and receive filter for colocated Multiple-Input Multiple-Output radar equipped with one-bit digital-to-analogue converters (DACs). The problem is formulated as maximising the output signal-to-interference-plus-noise ratio in the presence of signal-dependent interferences, subject to a discrete constraint imposed by the waveform quantised with one-bit DACs. To cope with the challenging non-convex problem, an alternating maximisation framework is developed to optimise the transmit waveform and receive filter vectors in an iterative manner. More specifically, for a given transmit waveform vector, the analytical expression of the receive filter vector is first derived. Then, by fixing the receive filter, a biconvex relaxation method is employed to tackle the non-convex problem with respect to the transmit waveform vector. The performance of the proposed approach is demonstrated by numerical simulations in different circumstances.

关键词： filter design filter vector receive filter design MIMO radar colocated multiple-input multiple-output radar convex programming iterative methods transmit waveform vector output signal-to-interference-plus-noise ratio concave programming iterative manner numerical simulations discrete constraint digital-analogue conversion one-bit digital-to-analogue converters alternating maximisation framework one-bit DAC biconvex relaxation method signal-dependent interferences nonconvex problem

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