9 research outputs found
An Efficient Alternating Riemannian/Projected Gradient Descent Ascent Algorithm for Fair Principal Component Analysis
Fair principal component analysis (FPCA), a ubiquitous dimensionality
reduction technique in signal processing and machine learning, aims to find a
low-dimensional representation for a high-dimensional dataset in view of
fairness. The FPCA problem involves optimizing a non-convex and non-smooth
function over the Stiefel manifold. The state-of-the-art methods for solving
the problem are subgradient methods and semidefinite relaxation-based methods.
However, these two types of methods have their obvious limitations and thus are
only suitable for efficiently solving the FPCA problem in special scenarios.
This paper aims at developing efficient algorithms for solving the FPCA problem
in general, especially large-scale, settings. In this paper, we first transform
FPCA into a smooth non-convex linear minimax optimization problem over the
Stiefel manifold. To solve the above general problem, we propose an efficient
alternating Riemannian/projected gradient descent ascent (ARPGDA) algorithm,
which performs a Riemannian gradient descent step and an ordinary projected
gradient ascent step at each iteration. We prove that ARPGDA can find an
-stationary point of the above problem within
iterations. Simulation results show that,
compared with the state-of-the-art methods, our proposed ARPGDA algorithm can
achieve a better performance in terms of solution quality and speed for solving
the FPCA problems.Comment: 5 pages, 8 figures, submitted for possible publicatio
Globally Optimal Beamforming Design for Integrated Sensing and Communication Systems
In this paper, we propose a multi-input multi-output (MIMO) beamforming
transmit optimization model for joint radar sensing and multi-user
communications, where the design of the beamformers is formulated as an
optimization problem whose objective is a weighted combination of the sum rate
and the Cram\'{e}r-Rao bound (CRB), subject to the transmit power budget
constraint. The formulated problem is challenging to obtain a global solution,
because the sum rate maximization (SRM) problem itself (even without
considering the sensing metric) is known to be NP-hard. In this paper, we
propose an efficient global branch-and-bound algorithm for solving the
formulated problem based on the McCormick envelope relaxation and the
semidefinite relaxation (SDR) technique. The proposed algorithm is guaranteed
to find the global solution for the considered problem, and thus serves as an
important benchmark for performance evaluation of the existing local or
suboptimal algorithms for solving the same problem.Comment: 5 pages, 2 figures, submitted for possible publicatio
Dual-functional Cellular and Radar Transmission: Beyond Coexistence
We propose waveform design for a dual-functional multi-input-multi-output (MIMO) system, which carries out both radar target detection and multi-user communications using a single hardware platform. By enforcing both a constant modulus (CM) constraint and a similarity constraint with respect to referenced radar signals, we aim to minimize the downlink multiuser interference. Unlike conventional approaches which obtain suboptimal solutions to the generally NP-hard CM optimization problems involved, we propose a branch-and-bound method to efficiently find the global minimizer of the problem. Simulations show that the proposed algorithm significantly outperforms the state-of-art by achieving a favorable trade-off between radar and communication performance