arXiv research

The paper analyzes portfolio optimization with two risk measures.

Improved greedy 2-coordinate updates for optimization problems with constraints.

Paper proposes a new method to find approximate SOSP for nonconvex constrained optimization problems.

Method solves complex optimization problems with high probability bounds.

An algorithm solves optimization problems with large sample sets, improving worst-case complexity.

Eigen-decomposition simplifies quadratic programming with equality constraints.

A new algorithm solves constrained optimization problems with stochastic gradients.

Paper tackles efficient SGD methods for constrained bilevel optimization.

Let M be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E and let f be a smooth map of M into a Riemannian manifold N. An unknown state x in M is observed via X=x+su where s>0 is a small parameter and u is a white Gaussian noise. For a given smooth prior on M and smooth estimators g …

Houdini finds high-dimensional saddle points under few constraints.

Integrates prediction models into portfolio optimization for better asset allocation.

This paper solves the dual Minkowski problem for q-torsional rigidity.

Researchers prove uniqueness and continuity of solution to L_p dual Minkowski problem.

Solves a generalized dual Minkowski problem for specific values of q.

Dual martingales improve primal optimal stopping problem efficiency.

Study anisotropic inverse Gauss curvature flows and solve dual Orlicz Minkowski problems.

In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the …

New method solves constrained optimization problems efficiently.

A new neural network improves classification speed and robustness.

We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of $M$ data p…

Efficient algorithm solves best subset selection problem.

Paper solves dual Minkowski problem in 2D plane for specific curvature cases.

Optimizes subset selection in sparse learning problems.

We study projectively self-dual polygons and curves in the projective plane. Our results provide a partial answer to problem No 1994-17 in the book of Arnold's problems.

This paper discusses the numéraire-based utility maximization problem in markets with proportional transaction costs. In particular, the investor is required to liquidate all her position in stock at the terminal time. We first observe the stability of the primal and dual value functions as well as the convergence of t…

Study anisotropic flows without global terms and solve dual Orlicz Christoffel-Minkowski problems.

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in …

We introduce the dual isoperimetrix which solves the isoperimetric problem in the dual Brunn-Minkowski theory. We then show how the dual isoperimetrix is related to the isoperimetrix from the Brunn-Minkowski theory.

New algorithms solve convex-concave problems faster than previous methods.

New method solves a generalized Minkowski problem using a curvature flow.

Derives stability for curvature measure near constant density, proving dual Minkowski problem solutions.

Paper offers a dual formulation for consumption problem with multiplicative habit.

Study investigates duality and dual optimizers for various transport problems.

Derives a primal-dual MLSVD formulation for multilinear data.

Proposes a new algorithm for solving optimization problems with stochastic objectives and equality constraints.

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework an…

Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through convex duality, and implies notably that for certain problems, such…

Smooth even solutions found for a generalized convex geometry problem.

Drago optimizes DRO problems with faster convergence.

Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study sketching from an optimization point of view: we first show that the iterative Hessia…

The general volume of a star body, a notion that includes the usual volume, the $q$th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding new general dual Orlicz curvature measure is defined that specializes to the $(p,q)$-dual curvature measures introduced recently by Lutwak, Ya…

Study confirms the uniqueness of the unit sphere for a specific geometric problem.

In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual problems in terms of FBSDEs plus additional conditions. Such formulation then allows…

In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we anal…

Paper estimates diameter for Minkowski problem solutions.

The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints…

The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice $\cal{X}$ with a order unit. The primal problem is given as the supremum o…

This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the consumption and investment proble…