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Fenchel-Lagrange duality for DC infinite programs with inequality constraints

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2021年 391卷 113426-113426页

作者： Li, Gang Xu, Yinghong Qin, Zhenhua Zhejiang Sci Tech Univ Dept Math Hangzhou 310018 Peoples R China Zhejiang Inst Mech & Elect Engn Dept Informat Technol Hangzhou 310053 Peoples R China

In this paper, we consider a composite DC optimization problem with constraints described by an arbitrary (possibly infinite) number of DC inequalities. By using the properties of the epigraph of the conjugate functions, we introduce some new constraint qualifications, which completely characterize the weak (zero/strong/stable) Fenchel- Lagrange duality between the primal problem and its dual problem. As applications, we obtain the corresponding results for a conic programming problem with DC composite function, a DC infinite programming problem with inequality constraints, and a DC optimization problem with composite functions, respectively. (c) 2021 Elsevier B.V. All rights reserved.

关键词： DC optimization problem Fenchel-Lagrange duality Epigraph conic programming

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Limit state analysis of reinforced concrete slabs by dual adaptive yield design approaches

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2022年第11期65卷 310-310页

作者： Ho, Phuc L. H. Le, Canh, V Nguyen, Phuong H. Int Univ VNU HCM Dept Civil Engn Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam

This paper deals with adaptive mesh refinement for limit state analysis of reinforced concrete slabs. Two simple and efficient mesh refinement indicators are developed. Plastic dissipation power in terms of curvature rates is used as refinement indicator in the kinematic yield design. For pseudo-static yield design approach, a Nielsen yield function value-based refinement indicator is proposed. Various slabs with arbitrary geometries and boundary conditions are examined, showing that upper and pseudo-lower bounds on the actual collapse load factors are accurately computed with the optimal layout of elements, and hence minimizing computational effort. Collapse mechanisms in terms of plastic dissipation distribution (or element concentration) and moment fields at limit state, that are crucial information for slab design, are also presented.

关键词： Limit state analysis Dissipation-based indicator Moment-based indicator Yield-line patterns Limit state moments conic programming

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Dynamic Reconfiguration of Electrical Power Distribution Systems with Distributed Generation and Storage *

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IFAC-PapersOnLine 2015年第23期48卷 136-141页

作者： Branimir Novoselnik Mato Baotić University of Zagreb Faculty of Electrical Engineering and Computing Unska 3 HR-10000 Zagreb Croatia

In this paper we present a nonlinear model predictive control strategy for dynamic reconfiguration of electrical power distribution systems with distributed generation and storage. Even though power distribution systems are physically built as interconnected meshed networks, as a rule, they operate in a radial topology. The network topology can be modified by changing status of the line switches (opened/closed). The goal of the proposed control strategy is to find the optimal radial network topology and the optimal power references for the controllable generators and energy storage units that will minimize cumulative active power losses while satisfying operating constraints. By utilizing recent results on convex relaxation of the power flow constraints, the proposed dynamic reconfiguration algorithm can be formulated as a mixed-integer second order cone program. Furthermore, if polyhedral approximations of second order cones are used then the underlying optimization problem can be solved as a mixed-integer linear program. Performance of the algorithm is illustrated on a small simulation case study based on actual meteorological and consumption data.

关键词： model predictive control dynamic reconfiguration power distribution system optimal power flow convex relaxation mixed-integer programming conic programming

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Bearing capacity of ring footing on weak sand layer overlying a dense sand deposit

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GEOMECHANICS AND GEOENGINEERING-AN INTERNATIONAL JOURNAL 2021年第4期16卷 249-262页

作者： Das, Pragyan Paramita Khatri, Vishwas N. Dutta, Rakesh Kumar Indian Inst Technol ISM Dept Civil Engn Dhanbad Bihar India Natl Inst Technol Dept Civil Engn Hamirpur Himachal Prades India

The present paper deals with the numerical investigation on the ultimate bearing capacity of ring footing resting on loose sand overlying a dense sand deposit. The study followed the use of lower and upper bound finite element limit analysis in conjunction with second-order conic programming. The analysis was carried out by varying the thickness as well as the angle of internal friction of the top and the bottom sand layers for the ring footing with the variation in the radius (ratio of internal radius to external radius) ratio. The results were expressed in terms bearing capacity ratio, which was found to decrease with an increase in the thickness and the friction angle of the dense sand layer. Further, the results obtained from this study compared well with the data available from the literature.

关键词： Limit analysis finite element bearing capacity Mohr-Coulomb conic programming

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conic optimization for quadratic regression under sparse noise

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 7994-8029页

作者： Igor Molybog Ramtin Madani Javad Lavaei Department of Industrial Engineering and Operations Research University of California Berkeley CA Department of Electrical Engineering University of Texas Arlington TA

This paper is concerned with the quadratic regression problem, where the goal is to find the unknown state (numerical parameters) of a system modeled by a set of equations that are quadratic in the state. We focus on the setting when a subset of equations of fixed cardinality is subject to errors of arbitrary magnitudes (potentially adversarial). We develop two methods to address this problem, which are both based on conic optimization and are able to accept any available prior knowledge on the solution as an input. We derive sufficient conditions for guaranteeing the correct recovery of the unknown state for each method and show that one method provides a better accuracy while the other one scales better to large-scale systems. The obtained conditions consist in bounds on the number of bad measurements each method can tolerate without producing a nonzero estimation error. In the case when no prior knowledge is available, we develop an iterative-based conic optimization technique. It is proved that the proposed methods allow up to half of the total number of measurements to be grossly *** efficacy of the developed methods is demonstrated in different case studies, including data analytics for a European power grid.

关键词： nonlinear regression conic programming bad data detection

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A multiple-drone arc routing and mothership coordination problem

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COMPUTERS & OPERATIONS RESEARCH 2023年第1期159卷

作者： Amorosi, Lavinia Puerto, Justo Valverde, Carlos Sapienza Univ Rome Dept Stat Sci Rome Italy Univ Seville Dept Stat Sci & Operat Res Seville Spain

This paper considers the optimisation problems that arise in coordinating a tandem between a mothership vehicle and a fleet of drones. Each drone can be launched from the mothership to perform a task. After completing their tasks, the drones return to the mothership to recharge their batteries and be ready for a new task. Tasks consist of (partially) visiting graphs of a given length to provide some services or to carry out a surveillance/inspection activity. The goal is to minimise the overall time of travelling carried out by the mothership (makespan) while satisfying some requirements in terms of fractions of visits to the target graphs. In all cases, we develop exact formulations resorting to mixed-integer second-order cone programmes that are compared on a testbed of instances to assess their performance. We also develop a matheuristic algorithm that provides reasonable solutions. Computational experiments show the usefulness of our methodology in different scenarios.

关键词： Arc routing problems Networks Drones conic programming

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Yield Design of Reinforced Concrete Slabs Using a Numerical Equilibrium Formulation

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JOURNAL OF ENGINEERING MECHANICS 2017年第9期143卷 04017073-04017073页

作者： Le, Canh V. Ngo, Chanh T. Chu, Thang Q. Int Univ VNU HCM Dept Civil Engn Ho Chi Minh Vietnam Mien Tay Construct Univ Dept Civil Engn Ho Chi Minh Vietnam

This paper presents a numerical procedure based on equilibrium finite elements and conic programming for plastic collapse load computation of reinforced concrete slabs governed by the Nielsen yield criterion. Bending moment fields are approximated using the enhanced Morley elements with an added second-degree moment field, allowing exact equilibrium relations to be achieved when applying a uniform pressure to the slabs. conic programming, which is robust and efficient, is incorporated into the obtained discrete equilibrium formulation to ensure solutions can be obtained rapidly. Several slabs of arbitrary geometries and boundary conditions are examined, providing accurate collapse load multipliers and distributions of moment fields at the limit state. (C) 2017 American Society of Civil Engineers.

关键词： Limit state Yield design Equilibrium model Collapse load conic programming

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Rational dual certificates for weighted sums-of-squares polynomials with boundable bit size

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JOURNAL OF SYMBOLIC COMPUTATION 2024年 121卷

作者： Davis, Maria M. Papp, David North Carolina State Univ Dept Math Campus Box 8205 Raleigh NC 27695 USA

In Davis and Papp (2022), the authors introduced the concept of dual certificates of (weighted) sum-of-squares polynomials, which are vectors from the dual cone of weighted sums of squares (WSOS) polynomials that can be interpreted as nonnegativity certificates. This initial theoretical work showed that for every polynomial in the interior of a WSOS cone, there exists a rational dual certificate proving that the polynomial is WSOS. In this article, we analyze the complexity of rational dual certificates of WSOS polynomials by bounding the bit sizes of integer dual certificates as a function of parameters such as the degree and the number of variables of the polynomials, or their distance from the boundary of the cone. After providing a general bound, we explore several special cases, such as univariate polynomials nonnegative over the real line or a bounded interval, represented in different commonly used bases. We also provide an algorithm which runs in rational arithmetic and computes a rational certificate with boundable bit size for a WSOS lower bound of the input polynomial.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： Polynomial optimization Nonnegativity certificates Sums-of-squares decomposition Computational real algebraic geometry conic programming

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Cone-restricted information theory

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2024年第26期57卷 265302-265302页

作者： George, Ian Chitambar, Eric Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

The max-relative entropy and the conditional min-entropy of a quantum state plays a central role in one-shot and zero-error quantum information theory. One attractive feature of this quantity is that it can be expressed as an optimization over the cone of positive semidefinite operators. Recently, it was shown that when replacing this cone with the cone of separable operators, a new type of conditional min-entropy emerges that admits an operational interpretation in terms of communicating classical information over a quantum channel. In this work, we explore more deeply the idea of building information-theoretic quantities from different base cones and determine which results in quantum information theory rely upon the positive semidefinite cone and which can be generalized. In terms of asymptotic information processing, we find that the standard equipartition properties break down if a given cone fails to approximate the positive semidefinite cone sufficiently well. We also show that the near-equivalence of the smooth max and Hartley entropies breaks down in this setting. We present parallel results for the extended conditional min-entropy, which requires extending the notion of k-superpositive channels to superchannels. On the other hand, we show that for classical-quantum states the separable cone is sufficient to re-cover the asymptotic theory, thereby drawing a strong distinction between the fully and partial quantum settings. We also present operational uses of this framework. We show that the cone restricted min-entropy of a Choi operator captures a measure of entanglement-assisted noiseless classical communication using restricted measurements. We also introduce a novel min-entropy-like quantity that captures the conditions for when one quantum channel can be transformed into another using bistochastic pre-processing. Lastly, we relate this framework to general conic norms and their non-additivity. Throughout this work, we concretely study generalized entrop

关键词： quantum information theory quantum entropies conic programming convex geometry

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Real-time microgrid economic dispatch based on model predictive control strategy

Real-time microgrid economic dispatch based on model predict...

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“紫金论电”2017智能电网保护和运行控制国际学术研讨会

作者： Yan DU Wei PE Naishi CHEN Xianjun GE Hao XIAO Institute of Electrical Engineering Chinese Academy of SciencesBeijing 100190China University of C China Electric Power Research Institute Beijing 100192China University of Chinese Academy of Sciences Beijing 100049China

To deal with uncertainties of renewable energy,demand and price signals in real-time microgrid operation,this paper proposes a model predictive control strategy for microgrid economic dispatch,where hourly schedule is constantly optimized according to the current system state and latest forecast ***,implicit network topology of the microgrid and corresponding power flow constraints are considered,which leads to a mixed integer nonlinear optimal power flow *** the non-convexity feature of the original problem,the technique of conic programming is applied to efficiently crack the *** results from a reconstructed IEEE-33 bus system and comparisons with the routine day-ahead microgrid schedule sufficiently substantiate the effectiveness of the proposed MPC strategy and the conic programming method.

关键词： conic programming Economic dispatch(ED) Microgrid Mixed-integer nonlinear programming (MINLP) Model predictive control (MPC) Optimal power flow (OPF)

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