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Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第2期71卷 403-433页

作者： Kanno, Yoshihiro Univ Tokyo Math & Informat Ctr Hongo 7-3-1 Tokyo 1138656 Japan

The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very time-consuming. This paper presents an alternative formulation, semidefinite programming with complementarity constraints, and proposes an efficient heuristic. The proposed method is based upon the concave-convex procedure for difference-of-convex programming. It is shown that the method can often find a practically reasonable truss design within the computational cost of solving some dozen of convex optimization subproblems.

关键词： Robust optimization Design-dependent load Complementarity constraint Semidefinite programming difference-of-convex programming Concave-convex procedure

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Further properties of the forward-backward envelope with applications to difference-of-convex programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2017年第3期67卷 489-520页

作者： Liu, Tianxiang Pong, Ting Kei Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we further study the forward-backward envelope first introduced in Patrinos and Bemporad (Proceedings of the IEEE Conference on Decision and Control, pp 2358-2363, 2013) and Stella et al. (Comput Optim Appl, doi:10.1007/s10589-017-9912-y, 2017) for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the original problem for the corresponding forward-backward envelope to be a level-bounded and Kurdyka-Aojasiewicz function with an exponent of;these results are important for the efficient minimization of the forward-backward envelope by classical optimization algorithms. In addition, we demonstrate how to minimize some difference-of-convex regularized least squares problems by minimizing a suitably constructed forward-backward envelope. Our preliminary numerical results on randomly generated instances of large-scale regularized least squares problems (Yin et al. in SIAM J Sci Comput 37:A536-A563, 2015) illustrate that an implementation of this approach with a limited-memory BFGS scheme usually outperforms standard first-order methods such as the nonmonotone proximal gradient method in Wright et al. (IEEE Trans Signal Process 57:2479-2493, 2009).

关键词： Forward-backward envelope Kurdyka-Lojasiewicz property difference-of-convex programming

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Efficient Channel Estimation for RIS-Assisted sub-Terahertz Communication Systems via difference-of-convex programming

Efficient Channel Estimation for RIS-Assisted sub-Terahertz ...

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IEEE/CIC International Conference on Communications in China (ICCC)

作者： Liu, Kai-Hui Wan, Liangtian Yang, Weiwei Dongguan Univ Technol Dongguan Peoples R China Dalian Univ Technol Dalian Peoples R China

ISBN: (纸本)9798350378412

Reconfigurable intelligent surfaces or intelligent reflecting surfaces (IRS) is a promising solution to enhance the coverage and capacity of sub-Terahertz systems by changing the directions of impinging electromagnetic waves. The control of the IRS requires perfect channel state information. This work adopts a novel and efficient channel estimation method for the IRS-aided sub-Terahertz system using difference-of-convex programming. Different from most previous works assuming L-1 or L-0 regularization, this paper studies a difference-of-convex L-1 and L-2 function minimization problem to estimate more accurate and stable channel parameters. Moreover, a fast alternating direction method of multipliers based algorithm is introduced to solve this difference-of-convex L-1 and L-2 function minimization problem. Simulation results are provided to illustrate the effectiveness of the proposed method.

关键词： Millimeter-wave/terahertz RIS/IRS channel estimation difference-of-convex programming ADMM

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Encoding inductive invariants as barrier certificates: Synthesis via difference-of-convex programming

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INFORMATION AND COMPUTATION 2022年第PartA期289卷

作者： Wang, Qiuye Chen, Mingshuai Xue, Bai Zhan, Naijun Katoen, Joost-Pieter Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing Peoples R China Univ Chinese Acad Sci Beijing Peoples R China Rhein Westfal TH Aachen Aachen Germany Chinese Acad Sci Inst Software Sci & Technol Integrated Informat Syst Lab Beijing Peoples R China

We present the invariant barrier-certificate condition that witnesses unbounded-time safety of differential dynamical systems. The proposed condition is the weakest possible one to attain inductive invariance. We show that discharging the invariant barrier-certificate condition - thereby synthesizing invariant barrier certificates - can be encoded as solving an optimization problem subject to bilinear matrix inequalities (BMIs). We further propose a synthesis algorithm based on difference-of-convex programming, which approaches a local optimum of the BMI problem via solving a series of convex optimization problems. This algorithm is incorporated in a branch-and-bound framework that searches for the global optimum in a divide-and-conquer fashion. We present a weak completeness result of our method, namely, a barrier certificate is guaranteed to be found (under some mild assumptions) whenever there exists an inductive invariant (in the form of a given template) that suffices to certify safety. Experimental results on benchmarks demonstrate the effectiveness and efficiency of our approach. (c) 2022 Elsevier Inc. All rights reserved.

关键词： Barrier certificates Inductive invariants Bilinear matrix inequalities difference-of-convex programming Semidefinite programming

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Reconfigurable Intelligent Surface for Green Edge Inference

IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING

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IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING 2021年第2期5卷 964-979页

作者： Hua, Sheng Zhou, Yong Yang, Kai Shi, Yuanming Wang, Kunlun ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China Chinese Acad Sci Shanghai Inst Microsyst & Informat Technol Shanghai 200050 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China JD Technol Grp Beijing 100176 Peoples R China East China Normal Univ Sch Commun & Elect Engn Shanghai 200241 Peoples R China

Reconfigurable intelligent surface (RIS) as an emerging cost-effective technology can enhance the spectral- and energy-efficiency of wireless networks. In this article, we consider an RIS-aided green edge inference system, where the inference tasks generated from resource-constrained mobile devices (MDs) are uploaded to and cooperatively performed at multiple resource-enhanced base stations (BSs). Taking into account both the computation and uplink/downlink transmit power consumption, we formulate an overall network power consumption minimization problem, which calls for the joint design of the set of tasks performed by each BS, uplink/downlink beamforming vectors of BSs, transmit power of MDs, and uplink/downlink phase-shift matrices at the RIS. However, the resulting combinatorial optimization problem is nonconvex and highly intractable. We tackle the challenge of combinatorial variables by exploiting the group sparsity structure of the beamforming vectors. Moreover, a block-structured optimization with mixed l(1,2)-norm and difference-of-convex-functions (DC) based three-stage framework is proposed to solve the problem, where the mixed l(1,2)-norm and DC techniques are adopted to induce the group sparsity structure and handle the nonconvex rank-one constraint, respectively. Simulations demonstrate the supreme performance gain of deploying an RIS and confirm the effectiveness of the proposed algorithm over the baseline algorithms in reducing the overall network power consumption.

关键词： Reconfigurable intelligent surface joint uplink and downlink green edge inference block-structured optimization difference-of-convex programming

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A three-operator splitting algorithm with deviations for generalized DC programming

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APPLIED NUMERICAL MATHEMATICS 2023年第1期191卷 62-74页

作者： Hu, Ziyue Dong, Qiao-Li Civil Aviat Univ China Tianjin Key Lab Adv Signal Proc Tianjin 300300 Peoples R China Civil Aviat Univ China Coll Sci Tianjin 300300 Peoples R China

In this paper, we introduce a three-operator splitting algorithm with deviations for solving the minimization problem composed of the sum of two convex functions minus a convex and smooth function in a real Hilbert space. The main feature of the proposed method is that two per-iteration deviation vectors provide additional degrees of freedom. We propose one-step and two step inertial three-operator splitting algorithms by selecting the deviations along a momentum direction. A numerical experiment for DC regularized sparse recovery problems shows that the proposed algorithms have better performance than the original three-operator splitting algorithm.(C) 2023 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： difference-of-convex programming Deviations Three-operator splitting algorithm Inertial algorithms

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Error Bound and Isocost Imply Linear Convergence of DCA-Based Algorithms to D-Stationarity

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第1期197卷 205-232页

作者： Tao, Min Li, Jiang-Ning Nanjing Univ Dept Math Natl Key Lab Novel Software Technol Nanjing Peoples R China Nanjing Univ Dept Math Nanjing Peoples R China

We consider a class of structured nonsmooth difference-of-convex minimization, which can be written as the difference of two convex functions possibly nonsmooth with the second one in the format of the maximum of a finite convex smooth functions. We propose two extrapolation proximal difference-of-convex-based algorithms for potential acceleration to converge to a weak/standard d-stationary point of the structured nonsmooth problem, and prove its linear convergence of these algorithms under the assumptions of piecewise error bound and piecewise isocost condition. As a product, we refine the linear convergence analysis of sDCA and epsilon-DCA in a recent work of Dong and Tao (J Optim Theory Appl 189: 190-220, 2021) by removing the assumption of locally linear regularity regarding the intersection of certain stationary sets and dominance regions. We also discuss sufficient conditions to guarantee these assumptions and illustrate that several sparse learning models satisfy all these assumptions. Finally, we conduct some elementary numerical simulations on sparse recovery to verify the theoretical results empirically.

关键词： difference-of-convex programming difference-of-convex algorithm Linear convergence Error bound

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Joint Latency and Cost Optimization for Erasure-Coded Data Center Storage

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IEEE-ACM TRANSACTIONS ON NETWORKING 2016年第4期24卷 2443-2457页

作者： Xiang, Yu Lan, Tian Aggarwal, Vaneet Chen, Yih-Farn R. George Washington Univ Dept Elect & Comp Engn Washington DC 20052 USA AT&T Labs Res Bedminster NJ 07921 USA Purdue Univ Sch Ind Engn W Lafayette IN 47907 USA

Modern distributed storage systems offer large capacity to satisfy the exponentially increasing need of storage space. They often use erasure codes to protect against disk and node failures to increase reliability, while trying to meet the latency requirements of the applications and clients. This paper provides an insightful upper bound on the average service delay of such erasure-coded storage with arbitrary service time distribution and consisting of multiple heterogeneous files. Not only does the result supersede known delay bounds that only work for a single file or homogeneous files, it also enables a novel problem of joint latency and storage cost minimization over three dimensions: selecting the erasure code, placement of encoded chunks, and optimizing scheduling policy. The problem is efficiently solved via the computation of a sequence of convex approximations with provable convergence. We further prototype our solution in an open-source cloud storage deployment over three geographically distributed data centers. Experimental results validate our theoretical delay analysis and show significant latency reduction, providing valuable insights into the proposed latency-cost tradeoff in erasure-coded storage.

关键词： Content placement data center difference-of-convex programming distributed storage erasure code gradient descent joint optimization latency Pollaczek-Kinchin transform queueing theory scheduling

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Optimal Power Flow of Radial Networks and Its Variations: A Sequential convex Optimization Approach

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IEEE TRANSACTIONS ON SMART GRID 2017年第6期8卷 2974-2987页

作者： Wei, Wei Wang, Jianhui Li, Na Mei, Shengwei Tsinghua Univ Dept Elect Engn State Key Lab Control & Simulat Power Syst & Gene Beijing 100084 Peoples R China Southern Methodist Univ Dept Elect Engn Dallas TX 75205 USA Argonne Natl Lab Energy Syst Div Argonne IL 60439 USA Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA

This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the e-constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method.

关键词： Bi-objective optimization convex optimization difference-of-convex programming maximum loadability optimal power flow radial network

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A refined inertial DC algorithm for DC programming

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OPTIMIZATION AND ENGINEERING 2023年第1期24卷 65-91页

作者： You, Yu Niu, Yi-Shuai Shanghai Jiao Tong Univ Sch Math Sci Shanghai Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Shanghai Jiao Tong Univ SJTU Paristech Shanghai Peoples R China

In this paper we consider the difference-of-convex (DC) programming problems, whose objective function is the difference of two convex functions. The classical DC Algorithm (DCA) is well-known for solving this kind of problems, which generally returns a critical point. Recently, an inertial DC algorithm (InDCA) equipped with heavy-ball inertial-force procedure was proposed in de Oliveira et al. (Set-Valued Variat Anal 27(4):895-919, 2019), which potentially helps to improve both the convergence speed and the solution quality. Based on InDCA, we propose a refined inertial DC algorithm (RInDCA) equipped with enlarged inertial step-size compared with InDCA. Empirically, larger step-size accelerates the convergence. We demonstrate the subsequential convergence of our refined version to a critical point. the Kurdyka-Lojasiewicz (KL) property of the objective function, we establish the sequential convergence of RInDCA. Numerical simulations on checking copositivity of matrices and image denoising problem show the benefit of larger step-size.

关键词： difference-of-convex programming Refined inertial DC algorithm Kurdyka-Lojasiewicz property Checking copositivity of matrices Image denoising

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