New boundary and point constraints for controlling conformal surfaces.
problem Controlling the geometry of surfaces defined by minimizers of conformal variational problems.
method Introducing new boundary conditions, point constraints, and flux constraints to control the metric and conformal scale factor.
result Introduces intuitive controls for exploring a subspace of conformal immersions.
Algorithm finds real line mapping from points under ordinal constraints.
problem Finding a mapping from points to real line under ordinal constraints.
method Approximation algorithm for dense case in O(n7)+(1/ε)O(1/ε1/8)n time. result Computes a solution satisfying (1−O(ε1/8))-fraction of all constraints. Houdini finds high-dimensional saddle points under few constraints.
problem Escaping from saddle points in high-dimensional spaces with constraints.
method Gradient descent methods under logarithmic inequality constraints.
result Polynomial time algorithms for escaping saddle points under constraints.
Study variational properties of curves in half-plane with area constraints.
problem Characterize critical points of inverse mean curvature.
method Variational analysis of curves with boundary constraints.
result Existence and stability of critical points with prescribed area.
The paper trains neural networks with robustness guarantees using semidefinite constraints.
problem Training neural networks with robustness and stability guarantees.
method Exploiting the banded structure of semidefinite constraints, an efficient and scalable training scheme based on interior point methods is set up.
result The method allows for enforcing Lipschitz constraints in large-scale deep neural networks, as demonstrated in numerical examples.
We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit fo…
In this paper, we study reinforcement learning (RL) algorithms to solve real-world decision problems with the objective of maximizing the long-term reward as well as satisfying cumulative constraints. We propose a novel first-order policy optimization method, Interior-point Policy Optimization (IPO), which augments the…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex sets. We propose a class of algorithms that perform both stochastic gradient desce…
The paper studies constraint maps with singularities and free boundaries, proving continuity near singularities and optimality.
problem Analyzing the structure of constraint maps with singularities and free boundaries.
method Establish continuity near singularities using a new quantitative unique continuation principle, and investigate the presence of branch points leading to new singularities.
result Topological singularities can only lie in the interior of the contact set in the uniformly convex setting, and the optimality of this result is proven.
Develops a first-order interior-point method for solving constrained variational inequalities.
problem Solving constrained variational inequalities with nontrivial constraints.
method ADMM-based interior-point method for constrained VIs (ACVI).
result First-order interior-point method with global convergence guarantees for general cVI problems.
The paper classifies constraint mappings in optimization problems.
problem Understanding generic behavior of constraint functions in optimization.
method Using singularity theory of smooth mappings and subgroup classification.
result Families of constraint mappings are a residual set with at most 4 parameters.
Proves critical points of ADM mass correspond to specific initial data sets.
problem Finding initial data sets with fixed Bartnik boundary data.
method Proves existence of critical points on a Banach manifold.
result Critical points of ADM mass correspond to initial data sets with generalized Killing vector fields.
New method solves optimization problems with stochastic objectives and constraints.
problem Optimization problems with stochastic objectives and deterministic constraints.
method Trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method.
result Global almost-sure convergence to first-order stationary points under standard assumptions.
We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with respect to boundary conditions on a multidimensional constraint variable, whose evo…
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept of half-continuity coupled with the introduction of local supersolutions. These…
We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on the stability of the obtained solutions with respect to preferred objective fun…
New methods reduce constraint violations to certainty in stochastic optimization.
problem Finding a point with certain constraint satisfaction and near-stationarity.
method Single-loop variance-reduced stochastic first-order methods with truncated momentum schemes.
result Achieves strong convergence guarantees for ε-stochastic stationary points with certain constraint satisfaction. Study circle actions on manifolds with 3 fixed points, finding dimension constraints and unique structures.
problem Characterize circle actions on oriented manifolds with exactly 3 fixed points.
method Analyzes manifold dimensions, isotropy submanifolds, and uses quaternionic projective space as a reference.
result For a manifold with three fixed points, its dimension must be a multiple of 4, and specific weights are unique.
New method upsamples sparse, non-uniform point clouds more accurately.
problem Suboptimal results from existing point cloud upsampling methods.
method Imposes manifold distribution constraints using Gaussian functions.
result Generates higher-quality, more uniformly distributed dense point clouds.
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy W=∫H2 under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the crit…
Geometrically characterizes virtual nonlinear nonholonomic constraints using symplectic methods.
problem Characterizing virtual nonlinear nonholonomic constraints geometrically.
method Geometric characterization using symplectic structures and Chetaev equations.
result A unique control law exists to satisfy virtual constraints, and closed-loop dynamics are projections of uncontrolled dynamics.
Paper shows affine constraint is unnecessary for high-dimensional data.
problem The necessity of an affine constraint in affine subspace clustering.
method Theoretical and empirical analysis of conditions for correctness of affine subspace clustering methods.
result Affine constraint has negligible effect on clustering performance for high-dimensional data.
Novel framework for efficient Gaussian process models with monotonicity constraints.
problem Improving predictive accuracy and reducing uncertainty in high-dimensional problems with monotonicity constraints.
method Virtual point-based framework using regularized linear randomize-then-optimize (RLRTO) and No U-Turn Sampler (NUTS) for efficient sampling.
result Significant improvements in computational efficiency with the RLRTO method and NUTS enhancements.
We prove the analyticity of smooth critical points for O'Hara's knot energies Eα,p, with p=1 and 2<α<3, subject to a fixed length constraint. This implies, together with the main result in \cite{BR13}, that bounded energy critical points of Eα,1 subject to a fixed length constraint ar…
New method solves stochastic optimization problems with random models.
problem Optimizing stochastic objectives with deterministic constraints.
method Trust-Region Sequential Quadratic Programming with random model.
result Global convergence guarantees for first- and second-order stationary points.
Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.
problem Minimizing loss and constraint violations in online convex optimization with smooth penalties.
method Projected gradient descent over a set around the current action.
result Both dynamic regret and constraint violation are bounded by the path-length.
New methods solve saddle point problems without line search.
problem Solving saddle point problems efficiently and adaptively.
method Auto-conditioned primal-dual hybrid gradient (AC-PDHG) and auto-conditioned ADMM (AC-ADMM) methods.
result Methods achieve optimal complexity and convergence guarantees.
A new model improves uncertainty estimation in deep learning.
problem Deep Kernel Learning (DKL) produces unreliable uncertainty estimates.
method Proposed a bi-Lipschitz constraint to preserve distances in feature space.
result DUE model outperforms previous DKL and other methods in uncertainty quality.
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained s…
Bayesian Optimization tackles hidden constraints in architecture optimization.
problem Optimizing system architectures with hidden constraints using expensive physics-based simulations.
method Surrogate-based optimization with Gaussian Process models, including strategies for handling failed evaluations.
result Best performance achieved with a mixed-discrete GP predicting Probability of Viability (PoV) and minimum PoV threshold selection.
As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant attention, especially the problem of pairwise constraint propagation. At least two reaso…
Simplifies neural network constraints with computationally efficient method.
problem Implementing hard output constraints in neural networks.
method Additional neural network layer for output constraints.
result Computational simplicity with complexity O(n*m) for linear constraints.
VRSGT algorithm reduces orthogonality constraints in decentralized optimization.
problem Decentralized optimization with orthogonality constraints.
method VRSGT algorithm with variance reduction and orthogonal techniques.
result VRSGT achieves convergence rate of O(1 / k) for orthogonality constraints.
An algorithm simplifies optimization with nonnegative and orthogonal constraints.
problem Optimization problems with nonnegative and orthogonal constraints.
method Support-set algorithm exploiting structural sparsity.
result Global convergence to first-order stationary point with iteration complexity O(ε−2). Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information beyond just values at some inputs, but also effectively constrain the search space. …
Study financial market graphs with Laplacian constraints.
problem Learning undirected graphs in financial markets.
method Proposes algorithms to estimate graphs accounting for financial data properties.
result Guidelines for estimating graphs in financial markets.
We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of the…
Modeling consumption and investment decisions with reference point and drawdown constraints.
problem Modeling consumption and investment decisions with reference point and drawdown constraints.
method Solving a stochastic control problem to derive value function, optimal consumption plan, and investment strategy in semi-explicit forms.
result Five important thresholds of wealth, all as functions of h, and significant economic implications. Optimal control problems on Riemannian manifolds are solved by penalizing constraint violations.
problem Optimal control problems with velocity constraints on Riemannian manifolds.
method Penalizing constraint violations and showing convergence to hard-constrained solutions.
result Solutions to soft-constrained problems converge to solutions of hard-constrained problems as penalty parameter increases.
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
problem Analyzing nonholonomic constraints in Hamiltonian systems.
method Deriving distributional RCH systems, geometric constraint conditions, and Hamilton-Jacobi theorems.
result Derives precise geometric constraint conditions and Hamilton-Jacobi theorems for nonholonomic systems.
The paper studies the properties of maps with free boundaries, focusing on the obstacle case.
problem Properties of the projected image and its regularity in maps with free boundaries.
method Dividing the map into distance and projected image parts; applying classical obstacle problem methods and proving higher regularity for the projected image.
result The projected image is at most of class C2,1 and globally of class W3,BMO, locally of C2,1 around the regular part of the free boundary. New method uses logical relations to derive bounds and inequality constraints from causal models.
problem Recovering bounds and inequality constraints from unobserved confounding.
method Using rules of probability and restrictions on counterfactuals implied by causal graphical models.
result Powerful method to recover known and novel bounds and constraints.
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail.
Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework, drawing on tools from the manifold reconstruction literature, to analyze the high-…
Wide deep neural networks are easy to optimize without constraints.
problem Optimizing wide deep neural networks.
method Analysis of optimization landscapes and empirical-risk minimization.
result Wide neural networks have no confined points, making optimization easier.
Psychiatric neuroscience is increasingly aware of the need to define psychopathology in terms of abnormal neural computation. The central tool in this endeavour is the fitting of computational models to behavioural data. The most prominent example of this procedure is fitting reinforcement learning (RL) models to decis…
Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. …
Study on surfaces in Heisenberg group with constant mean curvature.
problem Constant mean curvature surfaces in the Heisenberg group.
method Proves surfaces in a neighborhood of non-umbilic points are solutions to a sinh-Gordon equation with a differential constraint.
result Surfaces in Heisenberg group with constant mean curvature described by solutions to sinh-Gordon equation.