A signal recovery method for compressive sensing under noisy measurements is proposed. The problem is formulated as a nonconvex nonsmooth constrained optimization problem that uses the smoothly clipped absolute deviat...
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ISBN:
(纸本)9781424494743
A signal recovery method for compressive sensing under noisy measurements is proposed. The problem is formulated as a nonconvex nonsmooth constrained optimization problem that uses the smoothly clipped absolute deviation ( SCAD) function to promote sparsity. Relaxation is employed by means of a series of local linear approximations (LLAs) of the SCAD in a constrained formulation. The relaxation is shown to converge to a minimum of the original nonconvex constrained optimization problem. In order to solve each nonsmooth convex relaxation problem, a second-orderconeprogramming (SOCP) formulation is used, which can be applied by using standard state-of-the-art SOCP solvers such as SeDuMi. Experimental results demonstrate that signals recovered using the proposed method exhibit reduced l(infinity) reconstruction error when compared with competing methods such as l(1)-Magic. Simulations demonstrate that significant reduction in the reconstruction error can be achieved with computational cost that is comparable to that required by the l(1)-Magic algorithm.
In this paper, we present the detailed rate analysis for cell-free massive multiple-input multiple-output (MIMO) systems over spatially correlated Rayleigh fading channels. Taking the realistic impairment effects of s...
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In this paper, we present the detailed rate analysis for cell-free massive multiple-input multiple-output (MIMO) systems over spatially correlated Rayleigh fading channels. Taking the realistic impairment effects of spatial channel correlation, pilot contamination, and channel estimation errors into account, the lower-bounds of the achievable rates for both the uplink and downlink are derived with the low-complexity linear processing such as matched filter and conjugate beamforming, which enable us to take cognizance of the impacts of transmitted power, and the number of access points (APs). Based on the derived rate results, the asymptotic performance analysis is then carried out. Besides, we propose the sophisticated max-min power allocation strategies taking the actual requirements into consideration to provide uniformly good service to all users. However, the objective functions of the two optimization problems are both non-concave. Fortunately, the former for uplink can be characterized as geometric programming (GP), whilst the latter for downlink merging the efficient tools of second-order-cone programming (SOCP). Lastly, the numerical results are shown to verify our analytical results and the effectiveness of the proposed max-min fairness algorithms.
The classical trust-region subproblem (TRS) minimizes a nonconvex quadratic objective over the unit ball. In this paper, we consider extensions of TRS having extra constraints. When two parallel cuts are added to TRS,...
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The classical trust-region subproblem (TRS) minimizes a nonconvex quadratic objective over the unit ball. In this paper, we consider extensions of TRS having extra constraints. When two parallel cuts are added to TRS, we show that the resulting nonconvex problem has an exact representation as a semidefinite program with additional linear and second-order-cone (SOC) constraints. For the case where an additional ellipsoidal constraint is added to TRS, resulting in the "two trust-region subproblem" (TTRS), we provide a new relaxation including SOC constraints that strengthens the usual semidefinite programming (SDP) relaxation.
Moment-based ambiguity sets are mostly used in distributionally robust chance constraints (DRCCs). Their conservatism can be reduced by imposing unimodality, but the known reformulations do not scale well. We propose ...
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Moment-based ambiguity sets are mostly used in distributionally robust chance constraints (DRCCs). Their conservatism can be reduced by imposing unimodality, but the known reformulations do not scale well. We propose a new ambiguity set tailored to unimodal and seemingly symmetric distributions by encoding unimodality-skewness information, which leads to conic reformulations of DRCCs that are more tractable than known ones based on semi-definite programs. Besides, the conic reformulation yields a closed-form expression of the inverse of unimodal Cantelli's bound. (C) 2022 Elsevier B.V. All rights reserved.
A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-t...
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A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-that the convex hull of the intersection of an ellipsoid, , and a split disjunction, with , equals the intersection of with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form and , where is a SOCr cone, is a nonconvex cone defined by a single homogeneous quadratic, and H is an affine hyperplane. Under several easy-to-verify conditions, we derive simple, computable convex relaxations and , where is a SOCr cone. Under further conditions, we prove that these two sets capture precisely the corresponding conic/convex hulls. Our approach unifies and extends previous results, and we illustrate its applicability and generality with many examples.
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