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A SUCCESSIVE QUADRATIC PROGRAMMING ALGORITHM FOR SDP RELAXATION OF THE BINARY QUADRATIC PROGRAMMING
MU XUEWEN,LID SANYANG,ZHANG YALING Korean Mathematical Society 2005 대한수학회보 Vol.42 No.4
In this paper, we obtain a successive quadratic programming algorithm for solving the semidefinite programming (SDP) relaxation of the binary quadratic programming. Combining with a randomized method of Goemans and Williamson, it provides an efficient approximation for the binary quadratic programming. Furthermore, its convergence result is given. At last, We report some numerical examples to compare our method with the interior-point method on Maxcut problem.
Hong, Sung-Pil,Tunç,el, Levent Elsevier 2008 Discrete Applied Mathematics Vol.156 No.1
<P><B>Abstract</B></P><P>We present a unifying framework to establish a lower bound on the number of semidefinite-programming-based lift-and-project iterations (rank) for computing the convex hull of the feasible solutions of various combinatorial optimization problems. This framework is based on the maps which are commutative with the lift-and-project operators. Some special commutative maps were originally observed by Lovász and Schrijver and have been used usually implicitly in the previous lower-bound analyses. In this paper, we formalize the lift-and-project commutative maps and propose a general framework for lower-bound analysis, in which we can recapture many of the previous lower-bound results on the lift-and-project ranks.</P>
Stability of Nonlinear Hybrid Dynamical Systems with Time Delay via Sum of Squares Decomposition
Mohammad Ali Badamchizadeh,Sohrab Khanmohammadi,Gasem Alizadeh,Ali Aghagolzadeh 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.3
Considering an infinite number of eigenvalues for time delay systems, it is difficult to determine their stability. We have developed a new approach for the stability test of time delay nonlinear hybrid systems. Construction of Lyapunov functions for hybrid systems is generally a difficult task, but once these functions are found, stability’s analysis of the system is straight-forward. In this paper both delay-independent and delay-dependent stability tests are proposed, based on the construction of ap-propriate Lyapunov-Krasovskii functionals. The methodology is based on the sum of squares decom-position of multivariate polynomials and the algorithmic construction is achieved through the use of semidefinite programming. The reduction techniques provide numerical solution of large-scale in-stances; otherwise they will be computationally infeasible to solve. The introduced method can be used for hybrid systems with linear or nonlinear vector fields. Finally simulation results show the correct-ness and validity of the designed method.
Array pattern synthesis using semidefinite programming and a bisection method
이종호,최정식,이웅희,송지호 한국전자통신연구원 2019 ETRI Journal Vol.41 No.5
In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as an SDP problem, it is known that an additional rank‐one constraint is generated inevitably and relaxed via semidefinite relaxation. If the solution to the relaxed SDP problem is not of rank one, then conventional SDP‐based array pattern synthesis approaches fail to obtain optimal solutions because the additional rank‐one constraint is not handled appropriately. To overcome this drawback, we adopted a bisection technique combined with a penalty function method. Numerical applications are presented to demonstrate the validity of the proposed scheme.
Cooperative Decode-and-Forward Relaying for Secure Multicasting
이종호,손일수,송성주,김용화 한국전자통신연구원 2016 ETRI Journal Vol.38 No.5
In this paper, secure multicasting with the help of cooperative decode-and-forward relays is considered for the case in which a source securely sends a common message to multiple destinations in the presence of a single eavesdropper. We show that the secrecy rate maximization problem in the secure multicasting scenario under an overall power constraint can be solved using semidefinite programing with semidefinite relaxation and a bisection technique. Further, a suboptimal approach using zero-forcing beamforming and linear programming based power allocation is also proposed. Numerical results illustrate the secrecy rates achieved by the proposed schemes under secure multicasting scenarios.
Reconstruction of structured models using incomplete measured data
Yan Yu,Bo Dong,Bo Yu 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.62 No.3
The model updating problems, which are to find the optimal approximation to the discrete quadratic model obtained by the finite element method, are critically important to the vibration analysis. In this paper, the structured model updating problem is considered, where the coefficient matrices are required to be symmetric and positive semidefinite, represent the interconnectivity of elements in the physical configuration and minimize the dynamics equations, and furthermore, due to the physical feasibility, the physical parameters should be positive. To the best of our knowledge, the model updating problem involving all these constraints has not been proposed in the existed literature. In this paper, based on the semidefinite programming technique, we design a general-purpose numerical algorithm for solving the structured model updating problems with incomplete measured data and present some numerical results to demonstrate the effectiveness of our method.
A Robust Adaptive Beamformer Based on Semidefinite Programming with Quadratic Constraints
Feng Shen,Jinyang Song 보안공학연구지원센터 2015 International Journal of Hybrid Information Techno Vol.8 No.2
A robust beamforming with quadratic constraints, formulated as a semidefinite programming (SDP) problem, is proposed in this paper. With this formulation, the constraints on magnitude response can be easily imposed on the adaptive beamformer. And the non-convex quadratic constraints can be transformed into linear constraints. Therefore, the proposed method can be robust against the steering direction error. In practice, there are many array imperfections except steering direction error. In order to resist all kinds of array imperfections, the adaptive beamformer based on worst-case optimization technique is proposed by minimizing the array output power with respect to the worst-case array imperfections. Simulation results demonstrate that the proposed method is effective and can achieve a better performance.
Design of GBSB Neural Network Using Solution Space Parameterization and Optimization Approach
Cho, Hy-uk,Im, Young-hee,Park, Joo-young,Moon, Jong-sup,Park, Dai-hee Korean Institute of Intelligent Systems 2001 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.1 No.1
In this paper, we propose a design method for GBSB (generalized brain-state-in-a-box) based associative memories. Based on the theoretical investigation about the properties of GBSB, we parameterize the solution space utilizing the limited number of parameters sufficient to represent the solution space and appropriate to be searched. Next we formulate the problem of finding a GBSB that can store the given pattern as stable states in the form of constrained optimization problems. Finally, we transform the constrained optimization problem into a SDP(semidefinite program), which can be solved by recently developed interior point methods. The applicability of the proposed method is illustrated via design examples.
INDEFINITE STOCHASTIC LQ CONTROL WITH CROSS TERM VIA SEMIDEFINITE PROGRAMMING
Luo, Chengxin,Feng, Enmin 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.13 No.1
An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.
Ellipsoidal bounds for static response of framed structures against interactive uncertainties
Kanno, Yoshihiro,Takewaki, Izuru Techno-Press 2008 Interaction and multiscale mechanics Vol.1 No.1
This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the $\mathcal{S}$-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.