arXiv:2606. 23939v1 Announce Type: cross Abstract: Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem.
arXiv:2503. 24075v4 Announce Type: replace-cross Abstract: Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints.
arXiv:2409. 08066v3 Announce Type: replace Abstract: The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control.
arXiv:2606. 13803v1 Announce Type: new Abstract: Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications.
arXiv:2512. 02494v2 Announce Type: replace Abstract: Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems.
arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.
arXiv:2607. 00095v1 Announce Type: cross Abstract: Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics.
arXiv:2607. 22467v1 Announce Type: new Abstract: Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve.
arXiv:2606. 01521v1 Announce Type: new Abstract: A central problem in machine learning is that models can achieve near-perfect training performance while generalizing substantially less well to unseen examples.
Dual-energy CT (DECT) exploits attenuation differences across different X-ray spectra to provide richer material information and has been widely used in medical imaging. While sparse-view acquisition can lower radiation exposure, it makes DECT material decomposition even more challenging, as the problem is nonlinear and ill-posed.
arXiv:2601. 21487v2 Announce Type: replace-cross Abstract: We study minimization of smooth functions over feasible sets that have smooth embedded-manifold structure throughout or only on selected regions, using linear minimization oracles (LMOs) to determine search directions under user-chosen norms.
arXiv:2607. 23480v1 Announce Type: new Abstract: Variational autoencoders (VAEs) transform high-dimensional, often noisy data into a compact latent representation, making downstream optimization more tractable.
arXiv:2606. 05247v1 Announce Type: new Abstract: Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints.