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Conventional learning methods simplify the bilinear model by regarding two intrinsically coupled factors independently, which degrades the optimization procedure. One reason lies in the insufficient training due to the asynchronous gradient…
This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the…
In this paper, we present a novel stochastic optimization method, which uses the binary search technique with first order gradient based optimization method, called Binary Search Gradient Optimization (BSG) or BiGrad. In this optimization…
In this letter, we propose a novel manifold-based algorithm to solve the constant envelope (CE) precoding problem with interference exploitation. For a given power budget, we design the precoded symbols subject to the CE constraints, such…
Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs), enabling operations within constrained hardware without sacrificing performance. However, these…
This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…
We introduce Uniform Manifold Approximation with Two-phase Optimization (UMATO), a dimensionality reduction (DR) technique that improves UMAP to capture the global structure of high-dimensional data more accurately. In UMATO, optimization…
This work considers optimization of composition of functions in a nested form over Riemannian manifolds where each function contains an expectation. This type of problems is gaining popularity in applications such as policy evaluation in…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
In this letter, we investigate the hybrid beamforming based on deep reinforcement learning (DRL) for millimeter Wave (mmWave) multi-user (MU) multiple-input-single-output (MISO) system. A multi-agent DRL method is proposed to solve the…
In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation…
Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…
Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for…
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (i) To find a lower bound on the number of times that the…
Stein variational gradient descent (SVGD) is a prominent particle-based variational inference method used for sampling a target distribution. SVGD has attracted interest for application in machine-learning techniques such as Bayesian…
Distributed optimization has gained substantial interest in recent years due to its wide applications in machine learning. However, most of existing algorithms are designed for Euclidean spaces, leaving composite optimization on Riemannian…
We develop an efficient and near-optimal solution for beamforming in multi-user multiple-input-multiple-output single-hop wireless ad-hoc interference networks. Inspired by the weighted minimum mean squared error (WMMSE) method, a classical…
Massive arrays deployed in millimeter-wave systems enable high angular resolution performance, which in turn facilitates sub-meter localization services. Albeit suboptimal, up to now the most popular localization approach has been based on…
Reconfigurable distributed antenna and reflecting surface (RDARS) is a promising architecture for future sixth-generation (6G) wireless networks. In particular, the dynamic working mode configuration for the RDARS-aided system brings an…
Fast coverage of k-space is a major concern to speed up data acquisition in Magnetic Resonance Imaging (MRI) and limit image distortions due to long echo train durations. The hardware gradient constraints (magnitude, slew rate) must be…