Solves portfolio selection with constraints using martingale theory.
problem Portfolio selection with constraints on wealth and portfolio.
method Transformed into a mean-variance problem without constraints, solved using martingale theory.
result Directly presents semi-analytical expressions of efficient policy.
We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some …
Given a geodesic inside a simply-connected, complete, non-positively curved Riemannian (NPCR) manifold M, we get an associated geodesic inside the asymptotic cone Cone(M). Under mild hypotheses, we show that if the latter is contained inside a bi-Lipschitz flat, then the original geodesic supports a non-trivial, orthog…
Compact hypersurfaces minimize area in convex cones with free boundary.
problem Finding compact hypersurfaces minimizing area in convex cones with free boundary.
method Minimizing an anisotropic area functional under a volume constraint.
result Compact hypersurfaces are contained in a Wulff-shape.
Unified framework for hard affine SDP constraints in vRKHSs.
problem Incorporating shape constraints into predictive models for rich function classes.
method Unified convex optimization framework using second-order cone tightening.
result Unified and modular approach for handling multiple shape constraints.
New metrics found with cone singularities along line arrangements.
problem Existence of Calabi-Yau metrics with conical singularities.
method Ricci-flat Kähler metric with cone singularities along weighted line arrangements.
result Existence of a Ricci-flat Kähler metric with cone singularities.
The entropy-degree theorem applies to Alexandrov spaces with curvature constraints.
problem Geometric obstructions and volume bounds in singular spaces.
method Developed new degree theorem for Alexandrov spaces using integral currents.
result Entropy-volume minimization prevents metric singularities in Gromov-Hausdorff limits.
We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of Rn. Our result applies to…
The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a characteristic cone which are not zero in a neighbourhood of the vertex one can appeal to theorems due to Cagnac and Dossa…
The paper studies Ricci flow with specific curvature and volume constraints, proving convergence and curvature bounds.
problem Analyzing Ricci flow with Ricci curvature and volume constraints.
method Proving convergence and curvature bounds for Ricci flow with specific constraints.
result Ricci flow with specified constraints converges to a flat cone or static flow.
The paper studies how surfaces evolve in a cone under a specific flow.
problem Investigating the evolution of surfaces in a cone using a special flow.
method Analyzing a fully nonlinear parabolic Neumann problem under inverse curvature flow conditions.
result The evolving surfaces converge to a piece of the round sphere under certain conditions.
Conditions for polyhedral Kähler metrics on CP^n with specific singularities.
problem Existence of polyhedral Kähler metrics on complex projective space with specified singularities.
method Parabolic Kobayashi-Hitchin correspondence, linear and quadratic constraints on cone angles.
result Necessary and sufficient conditions for the existence of polyhedral Kähler metrics on CP^n.
SpodNet learns SPD matrices with structural constraints.
problem Estimating SPD matrices with additional structural constraints.
method Introduces SpodNet, a neural network module that guarantees SPD outputs and supports structural constraints.
result SpodNet learns SPD and sparse matrices effectively.
New method improves autofocus in CBCT scans by 93%.
problem Improper geometry information leads to misplaced signals in CBCT.
method Learning-based motion estimation combined with CBCT consistency constraint.
result Average artifact suppression of 93% achieved.
New method solves stochastic optimization problems with affine constraints.
problem Stochastic optimization problems with affine constraints.
method Stochastic Frank-Wolfe method.
result Guarantees convergence rates for objective residual and feasibility gap.
The classical Schläfli formula, and its ``higher'' analogs given in [SS03], are relations between the variations of the volumes and ``curvatures'' of faces of different dimensions of a polyhedra (which can be Euclidean, spherical or hyperbolic) under a first-order deformation. We describe here analogs of those formulas…
Paper proposes clustering algorithms for data from Union of Polyhedral Cones model.
problem Clustering data from multiple convex polyhedral cones.
method Sparse Subspace Clustering, Least squares approximation, K-nearest neighbor, Spectral Clustering.
result KNN outperforms NCL and LSA in clustering data from UOPC model.
We study constrained generalized Killing spinors over the metric cone and cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate certain problems arising in supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually…
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: Trading strategies must take values in a (possibly random and time-de…
Study optimal investment-reinsurance strategy for insurers under random coefficients and jumps.
problem Optimal investment-reinsurance strategy for insurers with random coefficients and jumps.
method Solves backward stochastic differential equations with jumps under a convex cone constraint.
result Optimal strategy and value remain the same even with random coefficients and jumps.
Study finds equivalence between MMV and MV preferences with conic constraints.
problem Monotone mean-variance portfolio selection under conic constraints.
method Closed-form solutions for optimal strategies under MMV and MV preferences.
result Optimal strategies coincide with and without the conic constraint.
This paper mainly aims to establish the well-posedness on time interval [0,ε−21T] of the classical initial problem for the bosonic membrane in the light cone gauge. Here ε is the small parameter measures the nonlinear effects. In geometric, the bosonic membrane are timelike submanifo…
The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed efficient policy may become inefficient when considering the corresponding trunc…
Researchers find H-convex functions for Heisenberg group sets.
problem Finding H-convex functions for H-convex sets in the Heisenberg group.
method Extension of Fenchel's convex family concept, employing precise conditions.
result Conditions on set shape for existence of H-convex functions.
Minimal splitting factors help study scalar curvature constraints.
problem Scalar curvature constraints in geometry.
method Introducing minimal splitting factors with positive scalar curvature.
result Minimal splitting factors have properties similar to area minimizing hypersurfaces.
The paper studies 4D Ricci flow manifolds with curvature constraints.
problem Investigating 4D Ricci flow manifolds with specific curvature conditions.
method Analyzing 4D manifolds with curvature constraints via Ricci flow.
result Proves topological and geometric gap theorems for maximal volume growth.
Study optimizes perimeter in convex domains with anisotropic constraints.
problem Optimizing perimeter in convex domains with anisotropic constraints.
method Analytical properties, topological features, and geometric measure theory results.
result Sharp isoperimetric inequalities and existence of minimizers.
Study examines how business units can benefit from group cohesion under regulatory constraints.
problem Regulatory constraints limit business units' ability to form a single cohesive group.
method Defined and analyzed cohesive risk measures to minimize capital costs.
result Cohesive risk measures allow groups to achieve minimal capital costs without altering individual liabilities.
In curved spaces, isoperimetric sets don't exist for small volumes.
problem Nonexistence of isoperimetric sets in spaces of positive curvature.
method Constructing specific noncompact smooth Riemannian manifolds with positive curvature.
result Nonexistence of isoperimetric sets for small volumes in spaces of positive curvature.
Robust MCVaR portfolio optimization using RKHS for risk management.
problem Minimizing portfolio risk while achieving higher returns under uncertainty.
method Introduces a robust MCVaR model with ellipsoidal support and RKHS uncertainty set for chance constraint.
result Robust model outperforms nominal and market portfolios in various market conditions.
Defines conditions for unique conformal metrics on manifolds with specific curvature properties.
problem Existence and uniqueness of conformal metrics with specified properties.
method Analyzes finite subsets of compact Riemannian manifolds with specific curvature constraints.
result Establishes necessary and sufficient conditions for existence and uniqueness of conformal metrics.
A new metric learning framework for signed graphs using Gershgorin disc alignment.
problem Learning Mahalanobis metrics from signed graphs efficiently.
method Proposes a fast metric learning framework using Gershgorin disc perfect alignment (GDPA) to circumvent full eigen-decomposition.
result Proves that Gershgorin disc left-ends of similarity transform are perfectly aligned at the smallest eigenvalue, enabling efficient optimization.
Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets of knots {K_i} that can arise as the links of singularities of cuspidal curves.…
In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a conically bounded convex set, i.e., an unbounded convex body admitting an \emph{exterior} asymptotic cone. Results concerning existence of isoperimetric regions, the behavior of the isoperimetric pr…
Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or rows) [1]. In real applications, however, such separability assumption is hard t…
Optimization with inequality constraints using embedded gradient vector field method
problem Optimization with inequality constraints
method Geometric framework using quadratic slack variables
result Derives Lagrange multiplier functions and second-order optimality conditions
The paper solves a finance problem using stochastic equations.
problem Risk minimization with portfolio constraints in financial markets.
method Uses Forward and Backward Stochastic Differential Equations (FBSDEs) to model and solve the problem.
result Explicit representations of solutions to quadratic risk minimization problems with constraints are derived.
Associative submanifolds of the 7-sphere S^7 are 3-dimensional minimal submanifolds which are the links of calibrated 4-dimensional cones in R^8 called Cayley cones. Examples of associative 3-folds are thus given by the links of complex and special Lagrangian cones in C^4, as well as Lagrangian submanifolds of the near…
We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their…
The paper tackles online resource allocation with uncertain coefficients and chance constraints.
problem Online stochastic resource allocation problem with chance constraints.
method Linearization and primal-dual algorithms with heuristic corrections.
result Optimality gap and constraint violation are on the order of √n.
Paper tackles hard shape constraints in kernel machines.
problem Enforcing shape requirements in a hard fashion is challenging.
method Tightened second-order cone constrained reformulation for kernel machines.
result Performance guarantees and efficiency demonstrated in various applications.
The paper proves positive energy-momentum theorems for charged AdS initial data sets.
problem Proving positive energy-momentum theorems for charged asymptotically AdS initial data sets.
method Introducing a charged energy-momentum functional and establishing positive theorems under a dominant energy condition.
result The charged energy-momentum functional is non-negative on a natural real cone.
For a k-flat F inside a locally compact CAT(0)-space X, we identify various conditions that ensure that F bounds a (k+1)-dimensional half flat in X. Our conditions are formulated in terms of the ultralimit of X. As applications, we obtain (1) constraints on the behavior of quasi-isometries between tocally compact CAT(0…
Extends compactness theory to variable-coefficient pseudo-differential operators on manifolds.
problem Compensated compactness for pseudodifferential operators on vector bundles.
method Establishes a theorem for weakly convergent sequences of sections under a pseudo-differential operator.
result Quadratic form converges in distributional sense under certain conditions.
The paper proves superhedging duality with transaction costs and frictions.
problem Superhedging under proportional transaction costs and model uncertainty.
method Quasi-sure setup with solvency cones, removing restrictive assumptions.
result Duality proved under more natural conditions of No Strict Arbitrage.
Investigates polynomial solutions to minimal surface equation, proving constraints and structure theorems.
problem Finding polynomial solutions to the minimal surface equation.
method Proves structure theorem, analyzes polynomial constraints, and uses eigenvalue estimates.
result Polynomial solutions must contain terms of both high and low degree, and have specific factorization properties.
We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of N-body solutions for the Einstein equation, which patently…
The paper proposes a control strategy for systems with sparse parameters using compressed sensing.
problem Control of linear systems with unknown sparse parameters under disturbances.
method Sparse estimation using Recursive Least Squares, improved with Basis Pursuit Denoising, and reformulated probabilistic constraints.
result The proposed algorithm outperforms existing methods in control design for systems with sparse impulse response parameters.