6,367 research outputs found
A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints
A computationally efficient method to solve non-convex programming problems
with linear equality constraints is presented. The proposed method is based on
a recursively feasible and descending sequential convex programming procedure
proven to converge to a locally optimal solution. Assuming that the first
convex problem in the sequence is feasible, these properties are obtained by
convexifying the non-convex cost and inequality constraints with inner-convex
approximations. Additionally, a computationally efficient method is introduced
to obtain inner-convex approximations based on Taylor series expansions. These
Taylor-based inner-convex approximations provide the overall algorithm with a
quadratic rate of convergence. The proposed method is capable of solving
problems of practical interest in real-time. This is illustrated with a
numerical simulation of an aerial vehicle trajectory optimization problem on
commercial-of-the-shelf embedded computers
Rank-Two Beamforming and Power Allocation in Multicasting Relay Networks
In this paper, we propose a novel single-group multicasting relay beamforming
scheme. We assume a source that transmits common messages via multiple
amplify-and-forward relays to multiple destinations. To increase the number of
degrees of freedom in the beamforming design, the relays process two received
signals jointly and transmit the Alamouti space-time block code over two
different beams. Furthermore, in contrast to the existing relay multicasting
scheme of the literature, we take into account the direct links from the source
to the destinations. We aim to maximize the lowest received quality-of-service
by choosing the proper relay weights and the ideal distribution of the power
resources in the network. To solve the corresponding optimization problem, we
propose an iterative algorithm which solves sequences of convex approximations
of the original non-convex optimization problem. Simulation results demonstrate
significant performance improvements of the proposed methods as compared with
the existing relay multicasting scheme of the literature and an algorithm based
on the popular semidefinite relaxation technique
A D.C. Programming Approach to the Sparse Generalized Eigenvalue Problem
In this paper, we consider the sparse eigenvalue problem wherein the goal is
to obtain a sparse solution to the generalized eigenvalue problem. We achieve
this by constraining the cardinality of the solution to the generalized
eigenvalue problem and obtain sparse principal component analysis (PCA), sparse
canonical correlation analysis (CCA) and sparse Fisher discriminant analysis
(FDA) as special cases. Unlike the -norm approximation to the
cardinality constraint, which previous methods have used in the context of
sparse PCA, we propose a tighter approximation that is related to the negative
log-likelihood of a Student's t-distribution. The problem is then framed as a
d.c. (difference of convex functions) program and is solved as a sequence of
convex programs by invoking the majorization-minimization method. The resulting
algorithm is proved to exhibit \emph{global convergence} behavior, i.e., for
any random initialization, the sequence (subsequence) of iterates generated by
the algorithm converges to a stationary point of the d.c. program. The
performance of the algorithm is empirically demonstrated on both sparse PCA
(finding few relevant genes that explain as much variance as possible in a
high-dimensional gene dataset) and sparse CCA (cross-language document
retrieval and vocabulary selection for music retrieval) applications.Comment: 40 page
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