We introduce convex and, in particular semidefinite optimization methods, duality, and complexity theory to shed new light on this relation. For the single stock problem, given moments of the prices ...

What are some recent advances in non-convex optimization research? This question was originally answered on Quora by Anima Anandkumar.

Researchers from SJTU have developed a convex-optimization-based quantum process tomography method for reconstructing quantum channels, and have shown the validity to seawater channels and general ...

Discover how ChatGPT 5 Pro AI shattered expectations by solving a decades-old math problem, marking a new era of AI-human collaboration.

Next we propose a tractable convex program based on regularized maximum-likelihood for model selection in this latent-variable setting; the regularizer uses both the ℓ₁ norm and the nuclear norm.

Even without convexity, this algorithm can be generically used as an oracle-efficient optimization algorithm, with accuracy evaluated empirically. We complement our theoretical results with an ...