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Outage Probability Based Robust Distributed Beam-Forming in Multi-User Cooperative Networks with Imperfect CSI

WIRELESS PERSONAL COMMUNICATIONS 2014年第3期77卷 1629-1658页

作者： Mahboobi, Behrad Soleimani-Nasab, Ehsan Ardebilipour, Mehrdad KN Toosi Univ Technol Fac Elect & Comp Engn Tehran *** Iran Grad Univ Adv Technol Fac Elect & Comp Engn Kerman *** Iran

In this paper, a new robust problem is proposed for relay beamforming in relay system with stochastic perturbation on channels of multi user and relay network. The robust problem aims to minimize the transmission power of relay nodes while the imperfect channel information (CSI) injects stochastic channel uncertainties to the parameters of optimization problem. In the power minimization framework, the relays amplification weights and phases are optimized assuming the availability of Gaussian channel distribution. The power sum of all relays is minimized while the outage probability of the instantaneous capacity (or SINR) at each link is above the outage capacity (or SINR) for each user. The robust problem is a nonconvex SDP problem with Rank constraint. Due to the nonconvexity of the original problem, three suboptimal problems are proposed. Simulation and numerical results are presented to compare the performance of the three proposed solutions with the existing worst case robust method.

关键词： Multiple unicast Relay beamforming Imperfect channel state information Penalty function conic quadratic programming Statistical robust optimization conic programming

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Limit analysis and lower/upper bounds to the macroscopic criterion of Drucker-Prager materials with spheroidal voids

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COMPTES RENDUS MECANIQUE 2014年第2期342卷 96-105页

作者： Pastor, Franck Kondo, Djimedo Athenee Royal Victor Horta Brussels Belgium UPMC CNRS UMR 7190 Inst Jean Le Rond dAlembert F-75252 Paris 05 France

The paper is devoted to a numerical Limit Analysis of a hollow spheroidal model with a Drucker-Prager solid matrix, for several values of the corresponding friction angle phi. In the first part of this study, the static and the mixed kinematic 3D-codes recently evaluated in [1] are modified to use the geometry defined in [2] for spheroidal cavities in the context of a von Mises matrix. The results in terms of macroscopic criteria are satisfactory for low and medium values of phi, but not enough for phi = 30 in the highly compressive part of the criterion. To improve these results, an original mixed approach, dedicated to the axisymmetric case, was elaborated with a specific discontinuous quadratic velocity field associated with the triangular finite element. Despite the less good conditioning inherent to the axisymmetric modelization, the resulting conic programming problem appears quite efficient, allowing one take into account numerical discretization refinements unreachable with the corresponding 3D mixed code. After a first validation in the case of spherical cavities whose exact solution is known, the final results for spheroidal voids are given for three usual values of the friction angle and two values of the cavity aspect factor. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

关键词： Gurson-type models Spheroidal voids Micromechanics Limit analysis Upper and lower bounds conic programming

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Adaptive computable approximation to cones of nonnegative quadratic functions

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OPTIMIZATION 2014年第6期63卷 955-980页

作者： Lu, Cheng Jin, Qingwei Fang, Shu-Cherng Wang, Zhenbo Xing, Wenxun Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Zhejiang Univ Dept Management Sci & Engn Hangzhou 310003 Zhejiang Peoples R China N Carolina State Univ Dept Ind & Syst Engn Raleigh NC 27695 USA Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

Cones of nonnegative quadratic functions are keys to the understanding of quadratic optimization problems, since any quadratically constrained quadratic programming problem can be reformulated as a linear conic programming problem over such a cone. This paper proposes an adaptive computable approximation scheme to cones of nonnegative quadratic functions and uses it for solving linear conic programming problems over such a cone. We study some basic properties of cones of nonnegative quadratic functions and present a class of simple cones with computable linear matrix inequalities representations. Building on these simple cones, we design a computable approximation scheme for handling a general cone of nonnegative quadratic functions. When the scheme is applied for solving linear conic programming problems over a cone of nonnegative quadratic functions, we incorporate an adaptive approach to enhance the performance of the proposed computable approximation scheme. The computational performance and theoretic convergence proof of the proposed adaptive computable approximation scheme are shown for solving box-constrained quadratic programming problems.

关键词： conic programming quadratic programming cones of nonnegative quadratic functions conic approximation lower bounds 49N15 49M37 90C26 90C20

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Regularity conditions characterizing Fenchel-Lagrange duality and Farkas-type results in DC infinite programming

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2014年第2期414卷 590-611页

作者： Sun, Xiang-Kai Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China

In this paper, we consider a DC infinite programming problem (P) with inequality constraints. By using the properties of the epigraph of the conjugate functions, we introduce some new notions of regularity conditions for (P). Under these new regularity conditions, we completely characterize the Fenchel-Lagrange duality and the stable Fenchel-Lagrange duality for (P). Similarly, we also completely characterize the Farkas-type results and the stable Farkas-type results for (P). As applications, we obtain the corresponding results for conic programming problems. (C) 2014 Elsevier Inc. All rights reserved.

关键词： DC infinite programming Regularity conditions Fenchel-Lagrange duality Farkas-type results conic programming

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SEPARATED CONTINUOUS conic programming: STRONG DUALITY AND AN APPROXIMATION ALGORITHM

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2009年第4期48卷 2118-2138页

作者： Wang, Xiaoqing Zhang, Shuzhong Yao, David D. Sun Yat Sen Univ Lingnan Univ Coll Guangzhou 510275 Guangdong Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China Columbia Univ Dept Ind Engn & Operat Res New York NY 10027 USA

Motivated by recent applications in robust optimization and in sign-constrained linear-quadratic control, we study in this paper a new class of optimization problems called separated continuous conic programming (SCCP). Focusing on a symmetric primal-dual pair, we develop a strong duality theory for the SCCP. Our idea is to use discretization to connect the SCCP and its dual to two ordinary conic programs. We show if the latter are strongly feasible and with finite optimal values, a condition that is readily veri. able, then the strong duality holds for the SCCP. This approach also leads to a polynomial-time approximation algorithm that solves the SCCP to any required accuracy.

关键词： continuous optimization conic programming duality approximation algorithm

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Central Swaths

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2013年第3期13卷 405-454页

作者： Renegar, James Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14850 USA

We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the "derivative cones" of a "hyperbolicity cone", the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path.

关键词： Hyperbolicity cone Hyperbolic polynomial Hyperbolic programming Central path conic programming Convex optimization

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Detecting copositivity of a symmetric matrix by an adaptive ellipsoid-based approximation scheme

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第1期229卷 21-28页

作者： Deng, Zhibin Fang, Shu-Cherng Jin, Qingwei Xing, Wenxun N Carolina State Univ Edward P Fitts Dept Ind & Syst Engn Raleigh NC 27695 USA Zhejiang Univ Dept Management Sci & Engn Hangzhou 310058 Zhejiang Peoples R China Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China

It is co-NP-complete to decide whether a given matrix is copositive or not. In this paper, this decision problem is transformed into a quadratic programming problem, which can be approximated by solving a sequence of linear conic programming problems defined on the dual cone of the cone of nonnegative quadratic functions over the union of a collection of ellipsoids. Using linear matrix inequalities (LMI) representations, each corresponding problem in the sequence can be solved via semidefinite programming. In order to speed up the convergence of the approximation sequence and to relieve the computational effort of solving linear conic programming problems, an adaptive approximation scheme is adopted to refine the union of ellipsoids. The lower and upper bounds of the transformed quadratic programming problem are used to determine the copositivity of the given matrix. (C) 2013 Elsevier B.V. All rights reserved.

关键词： conic programming Copositive Cone of nonnegative quadratic functions Adaptive approximation scheme

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A New Scheme for Guaranteed State Estimation of Power System

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IEEE TRANSACTIONS ON POWER SYSTEMS 2013年第4期28卷 4875-4876页

作者： Wang, Bin He, Guangyu Liu, Kaicheng Tsinghua Univ Beijing 100084 Peoples R China Shanghai Jiao Tong Univ Shanghai 200030 Peoples R China

Recent research has shown that the uncertainty intervals of state variables and measurements can be estimated by solving mathematical programming problems corresponding to the maximization or minimization of a component of these variables. However, the results are not guaranteed since the optimal problems are non-convex and the global optimal solutions cannot always be obtained. This paper presents a new scheme for guaranteed state estimation. Firstly, a conic programming is formulated to model these optimal problems by redefining variables and loosing the feasible space. Secondly, interval constraints propagation with all constraints concerned is applied to contract the solutions further to eliminate the pessimism. Comparisons are carried out, and results show that the result intervals are guaranteed and small enough for the control system with control dead zone concerned.

关键词： conic programming guaranteed state estimation interval constraints propagation

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Investment models based on clustered scenario trees

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期227卷 314-324页

作者： Wong, Man Hong Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

Stochastic programming is widely applied in financial decision problems. In particular, when we need to carry out the actual calculations for portfolio selection problems, we have to assign a value for each expected return and the associated conditional probability in advance. These estimated random parameters often rely on a scenario tree representing the distribution of the underlying asset returns. One of the drawbacks is that the estimated parameters may be deviated from the actual ones. Therefore, robustness is considered so as to cope with the issue of parameter inaccuracy. In view of this, we propose a clustered scenario-tree approach, which accommodates the parameter inaccuracy problem in the context of a scenario tree. (C) 2012 Elsevier B.V. All rights reserved.

关键词： conic programming Stochastic programming Interior point methods Robust optimization Scenario tree Portfolio selection

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Warmstarting the homogeneous and self-dual interior point method for linear and conic quadratic problems

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MATHEMATICAL programming COMPUTATION 2013年第1期5卷 1-25页

作者： Skajaa, Anders Andersen, Erling D. Ye, Yinyu Tech Univ Denmark Dept Informat & Math Modelling 2800 Kgs Lyngby Denmark MOSEK ApS DK-2100 Copenhagen Denmark Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

We present two strategies for warmstarting primal-dual interior point methods for the homogeneous self-dual model when applied to mixed linear and quadratic conic optimization problems. Common to both strategies is their use of only the final (optimal) iterate of the initial problem and their negligible computational cost. This is a major advantage when compared to previously suggested strategies that require a pool of iterates from the solution process of the initial problem. Consequently our strategies are better suited for users who use optimization algorithms as black-box routines which usually only output the final solution. Our two strategies differ in that one assumes knowledge only of the final primal solution while the other assumes the availability of both primal and dual solutions. We analyze the strategies and deduce conditions under which they result in improved theoretical worst-case complexity. We present extensive computational results showing work reductions when warmstarting compared to coldstarting in the range 30-75% depending on the problem class and magnitude of the problem perturbation. The computational experiments thus substantiate that the warmstarting strategies are useful in practice.

关键词： Warmstart Interior point method Homogeneous model conic programming

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