RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.
The Complex Gradient Operator and the CR-Calculus
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus. The presented material is suitable for exposition in an introductory Electrical Engineering graduate level course on the use of complex gradients and complex Hessian matrices, and has been successfully used in teaching at UC San Diego. Going beyond the commonly encountered treatments of the first-order complex vector calculus, second-order considerations are examined in some detail filling a gap in the pedagogic literature.
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Wirtinger-based Jacobian yields explicit singularity condition extended to all bus types, with bus-wise index C_W where min C_W,i > 1 certifies nonsingularity and gives a fast stability margin.
Framework transforms complex chance-constrained problems into convex SOCPs for individual constraints and uses copulas for joint constraints under moment, support, and data-driven ambiguity sets, demonstrated on beamforming.
Unified framework for complex zero-sum games with chance constraints that converts probabilistic constraints into convex second-order cone programs under various distribution assumptions.
Preconditioned ULA with exact likelihood enables faster, higher-quality posterior sampling for Cartesian and non-Cartesian MRI reconstructions than annealed sampling or DPS.
Presents complex versions of Fisher information matrices and Cramér-Rao bounds for quantum estimation depending on complex parameters.
CCV-QAOA is a new complex-valued continuous-variable variant of QAOA that solves real and complex multivariate optimization problems via a variational framework.
citing papers explorer
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Robust Uniform Recovery of Structured Signals from Nonlinear Observations
RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.
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A Wirtinger Power Flow Jacobian Singularity Condition for Voltage Stability in Converter-Rich Power Systems
Wirtinger-based Jacobian yields explicit singularity condition extended to all bus types, with bus-wise index C_W where min C_W,i > 1 certifies nonsingularity and gives a fast stability margin.
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Distributionally Robust Complex Chance-Constrained Optimization
Framework transforms complex chance-constrained problems into convex SOCPs for individual constraints and uses copulas for joint constraints under moment, support, and data-driven ambiguity sets, demonstrated on beamforming.
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Robust Chance Constrained Complex Zero-Sum Games
Unified framework for complex zero-sum games with chance constraints that converts probabilistic constraints into convex second-order cone programs under various distribution assumptions.
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Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm
Preconditioned ULA with exact likelihood enables faster, higher-quality posterior sampling for Cartesian and non-Cartesian MRI reconstructions than annealed sampling or DPS.
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Complex Field Formulation of the Quantum Estimation Theory
Presents complex versions of Fisher information matrices and Cramér-Rao bounds for quantum estimation depending on complex parameters.
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A Complex-Valued Continuous-Variable Quantum Approximation Optimization Algorithm (CCV-QAOA)
CCV-QAOA is a new complex-valued continuous-variable variant of QAOA that solves real and complex multivariate optimization problems via a variational framework.
- Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces