Related papers: Projection onto the capped simplex
In this paper, we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted $\ell_1$ (OWL1) norm ball. In particular, an efficient semismooth Newton method is proposed for solving the…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
Cooper and Long generalised Epstein and Penner's Euclidean cell decomposition of cusped hyperbolic manifolds of finite volume to non-compact strictly convex projective manifolds of finite volume. We show that Weeks' algorithm to compute…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been…
We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be…
Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical approximation of the polyconvex envelope. Instead of operating…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
We derive a closed-form expression for the projection onto a capped rotated second-order cone -- a convex set that arises in perspective relaxations of nonlinear programs with binary indicator variables. The closed-form solution involves…
In this paper we survey Eckardt points on a smooth complex cubic threefold with an approach aimed at computing all Eckardt points of a cubic threefold. In addition, we construct cubic threefolds with no Eckardt points but containing triple…
An important method to optimize a function on standard simplex is the active set algorithm, which requires the gradient of the function to be projected onto a hyperplane, with sign constraints on the variables that lie in the boundary of…
A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…
This paper documents a computational implementation of a {\em projection and rescaling algorithm} for finding most interior solutions to the pair of feasibility problems \[ \text{find} \; x\in L\cap\mathbb{R}^n_{+} \;\;\;\; \text{ and } \;…
We propose a method for learning and sampling from probability distributions supported on the simplex. Our approach maps the open simplex to Euclidean space via smooth bijections, leveraging the Aitchison geometry to define the mappings,…
We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…
Using sparse-inducing norms to learn robust models has received increasing attention from many fields for its attractive properties. Projection-based methods have been widely applied to learning tasks constrained by such norms. As a key…