New conic quadratic formulations improve outlier detection in regression models.
problem Detecting outliers in regression models with corrupted data.
method Deriving stronger second-order conic relaxations without big-M constraints.
result Proposed formulations are significantly faster than existing methods.
New formulations for comparing metric measure spaces with arbitrary positive measures.
problem Comparing metric measure spaces with arbitrary positive measures.
method Two novel formulations: a divergence and a conic lifting approach.
result Efficiently solvable formulations for comparing metric spaces with arbitrary positive measures.
Paper classifies conic submanifolds in control systems.
problem Characterizing and classifying conic submanifolds in control systems.
method Feedback equivalence of control-affine and fully nonlinear systems.
result Complete description of non-degenerate conic submanifolds.
In this paper, we consider a supervised learning setting where side knowledge is provided about the labels of unlabeled examples. The side knowledge has the effect of reducing the hypothesis space, leading to tighter generalization bounds, and thus possibly better generalization. We consider several types of side knowl…
Characterizes conical angles for metrics with dihedral symmetry.
problem Understanding metrics with specific symmetry properties.
method Using recent results on local invariants of quadratic differentials.
result Complete characterization of conical angles for dihedral spherical metrics.
We prove a formula for the determinant of Laplacian on an arbitrary compact polyhedral surface of genus one. This formula generalizes the well-known Ray-Singer result for a flat torus. A special case of flat conical metrics given by the modulus of a meromorphic quadratic differential on an elliptic surface is also cons…
We investigate the Lp-boundness of the Riesz transform on Riemannian manifolds whose Ricci curvature has quadratic decay. Two criteria for the Lp-unboundness of the Riesz transform are given. We recover known results about manifolds that are Euclidean or conical at infinity.
Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with ℓ0-"norm" constraints. Since such problems are non-convex and hard-to-solve, the standard approach is, instead, to tackle their convex surrogates based on ℓ1-norm relaxations. In this paper…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an ℓ0 constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper…
This paper introduces a new formulation of the Conic Gromov-Wasserstein distance for comparing complex network structures.
problem Comparing measures of unequal mass and complex network structures.
method Novel semi-coupling formulation and extension to hypernetworks.
result Establishes fundamental properties and robustness of CGW metric.
New method learns BN structures from data efficiently.
problem Learning sparse DAG structure of BN from continuous data.
method Consistent second-order conic integer programming with early stopping criterion.
result Near-optimal solutions to medium-size problems within reasonable time.
The paper discusses polynomial convergence to conical Kähler-Einstein metrics.
problem Understanding the convergence of Kähler-Einstein metrics to conical structures.
method Two-step degeneration theory and algebraic singularity analysis.
result Singular Kähler-Einstein metrics are conical if curvature grows quadratically near a point.
Paper proposes a QUBO formulation that reduces binary variables in Bayesian network learning.
problem Reducing the number of binary variables in QUBO formulations for Bayesian network learning.
method Proposes a new QUBO formulation that minimizes binary variables.
result Significantly reduces the number of binary variables required for Bayesian network structure learning.
Optimally estimates stability in Lorentzian isoperimetric inequalities.
problem Stability estimates in Lorentzian isoperimetric inequalities.
method Quantitative stability estimates using Fraenkel asymmetry and Lipschitz bounds.
result Optimal stability estimates with universal constants for Lorentzian isoperimetric inequalities.
The study connects conic connections and torsion-free principal connections on G-structures.
problem Relating torsion tensors of principal connections to characteristic conic connections.
method Formulating and verifying conditions for the existence of characteristic conic connections implying torsion-free principal connections.
result Conditions for the existence of characteristic conic connections imply the existence of torsion-free principal connections, verified for adjoint varieties of simple Lie algebras.
We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized residual function of [Busseti et al., 2018], the problem solution map is differentiabl…
Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.
problem Optimization problems involving rank-one convex functions with support constraints.
method Perspective reformulation techniques to exploit conic structure and establish convex hull results.
result Systematic perspective formulations for convex hull descriptions of sets with nonlinear separable or non-separable objective functions and combinatorial constraints.
Let X be a Banach space or more generally a complete metric space admitting a conical geodesic bicombing. We prove that every closed L-Lipschitz curve γ:S1→X may be extended to an L-Lipschitz map defined on the hemisphere f:H2→X. This implies that X satisfies a quadratic isoperimetri…
Study on finite energy SU(2) monopoles on AC 3-manifolds, proving integrality of charge and curvature decay.
problem Understanding the asymptotic behavior of finite energy SU(2) monopoles on AC 3-manifolds.
method Analysis of critical points of the SU(2) Yang--Mills--Higgs energy on asymptotically conical 3-manifolds.
result Proves integrality of the monopole number and quadratic decay of curvature, among other findings.
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under Möbius transformations. They can be obtained from discrete harmonic functions in the sense of the cotangent …
Study on conical Laplacian operators on Riemann surfaces, focusing on determinants and moduli spaces.
problem Analyzing determinants of Laplacian operators on Riemann surfaces with conical metrics.
method Introduce and compare two methods to regularize determinants of the conical Laplacian acting in the bundle K2. result Explicit expressions for the regularized determinants of the conical Laplacian in K2. A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational O(2) symmetry in a subspace orthogonal to a singular surface Σ so that the surfa…
In the generalized Legendre approach, the equation describing an asymptotically locally Euclidean space of type Dn is found to admit an algebraic formulation in terms of the group law on a Weierstrass cubic. This curve has the structure of a Cayley cubic for a pencil generated by two transversal plane conics, that i…
The paper pinches curvature in expanding Ricci solitons.
problem Curvature pinching in expanding Ricci solitons.
method Hamilton-Ivey type curvature pinching estimates.
result Three-dimensional Hamilton-Ivey type curvature pinching theorem.
New approach finds solutions to games with unbounded controls.
problem Existence of equilibrium in mean-field games with unbounded controls.
method Weak formulation and new existence/stability results for quadratic-growth generalized McKean-Vlasov BSDEs.
result Existence of equilibrium result for non-Markovian mean-field games with unbounded control space.
Paper solves curvature assignment on surfaces with sharp points and edges.
problem Prescribing curvatures on surfaces with conical singularities and corners.
method New variational formulation for surfaces with singularities.
result First results for prescribed curvatures on surfaces with singularities.
Moduli spaces of Abelian and quadratic differentials are stratified by multiplicities of zeroes; connected components of the strata correspond to ergodic components of the Teichmuller geodesic flow. It is known that the strata are not necessarily connected; the connected components were recently classified by M. Kontse…
Eigen-decomposition simplifies quadratic programming with equality constraints.
problem Optimizing solutions under linear equality constraints in quadratic programming.
method Eigenvalue decomposition of the quadratic term matrix to project optimal solutions.
result Established a linear mapping between EQP formulations with and without diagonalized Q. New method trains Boltzmann machines without supervision.
problem Training unsupervised learning models.
method Mixed binary quadratic feasibility problem formulation.
result Theory validated on XOR patterns.
This paper proves uniqueness of Kähler-Ricci flow on non-compact manifolds.
problem Uniqueness of asymptotically conical Kähler-Ricci flow on non-compact manifolds.
method Analysis of complete gradient expanding Kähler-Ricci solitons and their tangent cones.
result A complete solution to the Kähler-Ricci flow emerging from the soliton's tangent cone at infinity coincides with the forward self-similar Kähler-Ricci flow associated with the soliton.
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …
A streaming algorithm estimates quadratic covariation from financial data efficiently.
problem Estimating quadratic covariation from ultra-high-frequency financial data with limited memory.
method Formulated multi-scale, realized kernel, pre-averaging, and modulated realized covariance estimators with fixed bandwidth.
result Fixed bandwidth estimators require higher bandwidth for positive semidefiniteness.
SOC-ICNN expands neural network representational capacity by using conic optimization.
problem Restrictive representational capacity of ReLU-based ICNNs.
method Proposes SOC-ICNN architecture that uses Second-Order Cone Programming.
result SOC-ICNN strictly expands representational space without increasing complexity.
In this note we compare two recently proposed semidefinite relaxations for the sparse linear regression problem by Pilanci, Wainwright and El Ghaoui (Sparse learning via boolean relaxations, 2015) and Dong, Chen and Linderoth (Relaxation vs. Regularization A conic optimization perspective of statistical variable select…
We define a very general "parametric connect sum" construction which can be used to eliminate isolated conical singularities of Riemannian manifolds. We then show that various important analytic and elliptic estimates, formulated in terms of weighted Sobolev spaces, can be obtained independently of the parameters used …
This paper explores the geometric and topological properties of Poncelet porism for triangles.
problem Investigating the differential-geometric and topological properties of the Cayley condition in Poncelet porism for triangles.
method Demonstrated that the Cayley set is a smooth, connected, 9-dimensional complex manifold. Analyzed its structure through moduli spaces and fiber bundles.
result The Cayley set is a smooth, connected, 9-dimensional complex manifold.
The purpose of this paper is to generalize the convexity of Mabuchi's functional to the conic setting. We first established a frame to study conic cscK metrics, and then the conic Mabuchi functional was introduced in such a way that conic cscK metrics are its critical points. Finally we proved the convexity of the coni…
The paper classifies isoparametric hypersurfaces in conic Finsler spaces.
problem Identifying new isoparametric hypersurfaces in conic Finsler spaces.
method Introduced isoparametric functions and hypersurfaces in conic Finsler spaces, classified them in specific spaces.
result Found additional isoparametric hypersurfaces in conic Minkowski spaces, such as helicoids.
Develops an algorithm to find the best subset of points for maximizing the coefficient of determination.
problem Finding the optimal subset of points for maximizing the coefficient of determination in robust correlation analysis.
method The extit{quadratic sweep} method, which involves projecting points into \(\mathbb{R}^5\) and iterating over linearly separable \(k\)-subsets.
result The method optimally finds the best subset of points for maximizing the coefficient of determination without error over several million trials up to \(n=30\).
Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to a simple convex formulation, it suffers from several issues due to the loosenes…
In this paper we propose a tractable quadratic programming formulation for calculating the equilibrium term structure of electricity prices. We rely on a theoretical model described in [21], but extend it so that it reflects actually traded electricity contracts, transaction costs and liquidity considerations. Our nume…
Two unique conic-line arrangements with degree 9 are found.
problem Identifying Zariski pairs of conic-line arrangements.
method Using connected numbers to distinguish topologies.
result Found two pairs of conic-line arrangements with a unique conic.
Study conic singular manifolds, proving Lipschitz normal embedding.
problem Understanding metric properties of conic singular manifolds.
method Analyzing interplay between conic and asymptotically conic behavior.
result Proves Lipschitz normal embedding for conic singular sub-manifolds.
Novel method solves group synchronization with robust corruption tolerance.
problem Group synchronization with high corruption tolerance.
method Quadratic programming formulation exploiting cycle consistency.
result Global minimum recovers corruption levels under mild conditions.
The paper shows how to calculate risk-neutral default probabilities from bid and ask CDS quotes.
problem Calculating risk-neutral default probabilities from market quotes.
method Using conic finance framework and Poisson process to formulate and solve the calibration problem.
result A unique solution for risk-neutral default probabilities and implied liquidity.
Desingularizes conically singular Cayley submanifolds.
problem Constructing fibrations of compact Spin(7) manifolds by Cayley submanifolds.
method Desingularization through gluing rescaled asymptotically conical submanifolds.
result Conically singular Cayley submanifolds can be desingularized.
Quantizes Stäckel integrable systems into self-adjoint operators.
problem Quantizing Stäckel integrable systems into self-adjoint operators.
method Constructs commutative self-adjoint operators from quadratic Hamiltonians in involution.
result Proves multiplicative separation of variables for Stäckel integrable systems.
Develops second order infinitesimal structures on Teichmüller space.
problem Understand the infinitesimal structures of Teichmüller space.
method Formulated second order infinitesimal structures over Teichmüller space.
result Affirmative answers to two folklore problems on Teichmüller space.