arXiv research

Abstract: Survey on quadratic Hessian equations, their properties, and open problems.

Entire self-shrinking solutions on complex plane are rigid and come from quadratic potentials.

Solutions to a quadratic matrix equation are linked to strongly regular graphs and multiplicative characters.

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to simila…

Ancient Lagrangian flows get limited convex solutions.

Researchers prove entire self-shrinking solutions to Kähler-Ricci flow are quadratic.

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…

We calculate explicitly the quadratic solution to the WDVV equations corresponds to the quasi-Coxeter conjugacy class $E_8(a_1)$ using the associated classical $W$-algebra.

New method solves large-scale QCPs using low-discrepancy sequences.

Investigates quadratic-exponential growth BSDEs with jumps and proves existence and differentiability.

Solutions near infinity to special Lagrangian equations are asymptotic to quadratic polynomials with logarithmic terms.

A new algorithm for solving constrained convex optimization problems efficiently.

In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z,u). From a technical point of view, we use a direct fixed point approach as in Tevzadze [38], which allows us to obtain existence and unique…

Study shows uniqueness of solutions on complex manifolds without requiring solution decay.

V-matrix method fails to consistently estimate conditional probabilities.

The paper proves constant rank theorems for special Lagrangian equations.

In this note, we derive a Liouville theorem for the complex Monge-Ampère equation. Our result states that if the global solution $u$ of the complex Monge-Ampère equation with constant right-hand side differs from a quadratic polynomial solution by $o(\abs{x}^2)$ at infinity, then $u$ is a quadratic polynomial.

New representation of field equations for QMAG, presenting new solutions.

Paper finds unique viscosity solution to complex control problems.

Unique minimal surfaces near quadratic cones are identified.

Study of hyperkähler reduction on Riemann surfaces, finding more solutions.

New approach finds solutions to games with unbounded controls.

Over-parametrized networks with quadratic activations can find globally optimal solutions for convex losses.

Optimal trading speeds are reduced by small quadratic costs, with specific velocity regimes identified.

Eigen-decomposition simplifies quadratic programming with equality constraints.

We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resul…

Optimal contracts are found for agents with quadratic effort costs.

Minimum helicity states found in MHD equations.

Study how transaction costs impact stock returns and holdings in equilibrium.

We show that any global solution to the special Lagrangian equations with the phase larger than a critical value must be quadratic.

We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only …

Study solves HJB equations for time-inconsistent control problems.

The paper develops an expansion for optimizing portfolios with small quadratic transaction costs.

One-pass SGD dynamics in overparameterized quadratic networks show slow escape from poor solutions.

Proposes sparse QSVM for better generalization and interpretability.

Solves generalized twisted rabbit problems for higher degree polynomials.

Minimax solutions are weak solutions to Cauchy problems involving Hamilton--Jacobi equations, constructed from generating families quadratic at infinity of their geometric solutions. We give a complete description of minimax solutions and we classify their generic singularities of codimension not greater than 2.

The study classifies harmonic cubic polynomials in up to 4 dimensions.

This research proves that quadratic regularized optimal transport can approximate the Laplace-Beltrami operator on smooth manifolds.

Solves new quadratic BSDE systems for market performance analysis.

We show that every complete entire self-shrinking solution on complex Euclidean space to the Kahler-Ricci flow must be generated from a quadratic potential.

Develops a new optimization method for multi-slot ranking in social media.

Neural network discovers exact solutions to QP with linear constraints.

We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices …

Improves semi-supervised classification performance without strong assumptions.

Study Markov chain gradient descent in Hilbert spaces for quadratic loss.

We develop algorithms for the numerical computation of the quadratic hedging strategy in incomplete markets modeled by pure jump Markov process. Using the Hamilton-Jacobi-Bellman approach, the value function of the quadratic hedging problem can be related to a triangular system of parabolic partial integro-differential…

Efficiently solves heterogeneous QPs by reducing variables using instance-specific projections.