Proposes constraint manifolds with corners as a new topological structure for mixed-constraint optimization in robotics, enabling direct unconstrained optimization on the feasible set.
On manifolds with corners
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the subject are not agreed upon, there are several inequivalent definitions in use of manifolds with corners, of boundary, and of smooth map, depending on the applications in mind. We present a theory of manifolds with corners which includes a new notion of smooth map f : X --> Y. Compared to other definitions, our theory has the advantage of giving a category Man^c of manifolds with corners which is particularly well behaved as a category: it has products and direct products, boundaries behave in a functorial way, and there are simple conditions for the existence of fibre products X x_Z Y in Man^c. Our theory is tailored to future applications in Symplectic Geometry, and is part of a project to describe the geometric structure on moduli spaces of J-holomorphic curves in a new way. But we have written it as a separate paper as we believe it is of independent interest.
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The authors prove a formal Newlander-Nirenberg theorem for b-complex structures on manifolds with generalized corners, showing that the structure agrees with a standard model to infinite order along each corner stratum.
A Riemannian L-BFGS method with adapted Cauchy-point bound handling outperforms classical interior-point and L-BFGS-B solvers on mixed manifold-plus-bounds problems by orders of magnitude.
Susceptibilities quantify observable responses to data perturbations in statistical models, with estimators proven consistent and asymptotically unbiased for large n.
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CMC-Opt: Constraint Manifold with Corners for Inequality-Constrained Optimization
Proposes constraint manifolds with corners as a new topological structure for mixed-constraint optimization in robotics, enabling direct unconstrained optimization on the feasible set.
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B-complex manifolds with generalized corners. I. Newlander-Nirenberg Theorems
The authors prove a formal Newlander-Nirenberg theorem for b-complex structures on manifolds with generalized corners, showing that the structure agrees with a standard model to infinite order along each corner stratum.
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A Riemannian quasi-Newton algorithm for optimization with Euclidean bounds
A Riemannian L-BFGS method with adapted Cauchy-point bound handling outperforms classical interior-point and L-BFGS-B solvers on mixed manifold-plus-bounds problems by orders of magnitude.
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Linear Response Estimators for Singular Statistical Models
Susceptibilities quantify observable responses to data perturbations in statistical models, with estimators proven consistent and asymptotically unbiased for large n.