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math.OC2025
Reachability of gradient descent
Cédric Josz, Wenqing Ouyang
We show that gradient descent can converge to any local minimum of a smooth semi-algebraic function. This holds if the step sizes are nonsummable and sufficiently small. The same r…
math.OC2025
Kurdyka-Łojasiewicz exponent via square transformation
Wenqing Ouyang
We consider one of the most common reparameterization techniques, the square transformation. Assuming the original objective function is the sum of a smooth function and a polyhedr…
math.OC2025
Burer-Monteiro factorizability of nuclear norm regularized optimization
Wenqing Ouyang, Ting Kei Pong, Man-Chung Yue
This paper studies the relationship between the nuclear norm-regularized minimization problem, which minimizes the sum of a function and a positive multiple of the nuclea…