2,020 research outputs found
Achieving Global Optimality for Weighted Sum-Rate Maximization in the K-User Gaussian Interference Channel with Multiple Antennas
Characterizing the global maximum of weighted sum-rate (WSR) for the K-user
Gaussian interference channel (GIC), with the interference treated as Gaussian
noise, is a key problem in wireless communication. However, due to the users'
mutual interference, this problem is in general non-convex and thus cannot be
solved directly by conventional convex optimization techniques. In this paper,
by jointly utilizing the monotonic optimization and rate profile techniques, we
develop a new framework to obtain the globally optimal power control and/or
beamforming solutions to the WSR maximization problems for the GICs with
single-antenna transmitters and single-antenna receivers (SISO), single-antenna
transmitters and multi-antenna receivers (SIMO), or multi-antenna transmitters
and single-antenna receivers (MISO). Different from prior work, this paper
proposes to maximize the WSR in the achievable rate region of the GIC directly
by exploiting the facts that the achievable rate region is a "normal" set and
the users' WSR is a "strictly increasing" function over the rate region.
Consequently, the WSR maximization is shown to be in the form of monotonic
optimization over a normal set and thus can be solved globally optimally by the
existing outer polyblock approximation algorithm. However, an essential step in
the algorithm hinges on how to efficiently characterize the intersection point
on the Pareto boundary of the achievable rate region with any prescribed "rate
profile" vector. This paper shows that such a problem can be transformed into a
sequence of signal-to-interference-plus-noise ratio (SINR) feasibility
problems, which can be solved efficiently by existing techniques. Numerical
results validate that the proposed algorithms can achieve the global WSR
maximum for the SISO, SIMO or MISO GIC.Comment: This is the longer version of a paper to appear in IEEE Transactions
on Wireless Communication
Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems
Ensuring solution feasibility is a key challenge in developing Deep Neural
Network (DNN) schemes for solving constrained optimization problems, due to
inherent DNN prediction errors. In this paper, we propose a "preventive
learning'" framework to systematically guarantee DNN solution feasibility for
problems with convex constraints and general objective functions. We first
apply a predict-and-reconstruct design to not only guarantee equality
constraints but also exploit them to reduce the number of variables to be
predicted by DNN. Then, as a key methodological contribution, we systematically
calibrate inequality constraints used in DNN training, thereby anticipating
prediction errors and ensuring the resulting solutions remain feasible. We
characterize the calibration magnitudes and the DNN size sufficient for
ensuring universal feasibility. We propose a new Adversary-Sample Aware
training algorithm to improve DNN's optimality performance without sacrificing
feasibility guarantee. Overall, the framework provides two DNNs. The first one
from characterizing the sufficient DNN size can guarantee universal feasibility
while the other from the proposed training algorithm further improves
optimality and maintains DNN's universal feasibility simultaneously. We apply
the preventive learning framework to develop DeepOPF+ for solving the essential
DC optimal power flow problem in grid operation. It improves over existing
DNN-based schemes in ensuring feasibility and attaining consistent desirable
speedup performance in both light-load and heavy-load regimes. Simulation
results over IEEE Case-30/118/300 test cases show that DeepOPF+ generates
feasible solutions with 0.5% optimality loss and up to two orders of
magnitude computational speedup, as compared to a state-of-the-art iterative
solver.Comment: 43pages, 9 figures. In submissio
Artificial Noise-Aided Biobjective Transmitter Optimization for Service Integration in Multi-User MIMO Gaussian Broadcast Channel
This paper considers an artificial noise (AN)-aided transmit design for
multi-user MIMO systems with integrated services. Specifically, two sorts of
service messages are combined and served simultaneously: one multicast message
intended for all receivers and one confidential message intended for only one
receiver and required to be perfectly secure from other unauthorized receivers.
Our interest lies in the joint design of input covariances of the multicast
message, confidential message and artificial noise (AN), such that the
achievable secrecy rate and multicast rate are simultaneously maximized. This
problem is identified as a secrecy rate region maximization (SRRM) problem in
the context of physical-layer service integration. Since this bi-objective
optimization problem is inherently complex to solve, we put forward two
different scalarization methods to convert it into a scalar optimization
problem. First, we propose to prefix the multicast rate as a constant, and
accordingly, the primal biobjective problem is converted into a secrecy rate
maximization (SRM) problem with quality of multicast service (QoMS) constraint.
By varying the constant, we can obtain different Pareto optimal points. The
resulting SRM problem can be iteratively solved via a provably convergent
difference-of-concave (DC) algorithm. In the second method, we aim to maximize
the weighted sum of the secrecy rate and the multicast rate. Through varying
the weighted vector, one can also obtain different Pareto optimal points. We
show that this weighted sum rate maximization (WSRM) problem can be recast into
a primal decomposable form, which is amenable to alternating optimization (AO).
Then we compare these two scalarization methods in terms of their overall
performance and computational complexity via theoretical analysis as well as
numerical simulation, based on which new insights can be drawn.Comment: 14 pages, 5 figure
Functional Inequalities in the Absence of Convexity and Lower Semicontinuity with Applications to Optimization
In this paper we extend some results in [Dinh, Goberna, López, and Volle, Set-Valued Var. Anal., to appear] to the setting of functional inequalities when the standard assumptions of convexity and lower semicontinuity of the involved mappings are absent. This extension is achieved under certain condition relative to the second conjugate of the involved functions. The main result of this paper, Theorem 1, is applied to derive some subdifferential calculus rules and different generalizations of the Farkas lemma for nonconvex systems, as well as some optimality conditions and duality theory for infinite nonconvex optimization problems. Several examples are given to illustrate the significance of the main results and also to point out the potential of their applications to get various extensions of Farkas-type results and to the study of other classes of problems such as variational inequalities and equilibrium models.This research was partially supported by MICINN of Spain, grant MTM2008-06695-C03-01
DC Proximal Newton for Non-Convex Optimization Problems
We introduce a novel algorithm for solving learning problems where both the
loss function and the regularizer are non-convex but belong to the class of
difference of convex (DC) functions. Our contribution is a new general purpose
proximal Newton algorithm that is able to deal with such a situation. The
algorithm consists in obtaining a descent direction from an approximation of
the loss function and then in performing a line search to ensure sufficient
descent. A theoretical analysis is provided showing that the iterates of the
proposed algorithm {admit} as limit points stationary points of the DC
objective function. Numerical experiments show that our approach is more
efficient than current state of the art for a problem with a convex loss
functions and non-convex regularizer. We have also illustrated the benefit of
our algorithm in high-dimensional transductive learning problem where both loss
function and regularizers are non-convex
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