Related papers: How to project onto the monotone nonnegative cone …
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
A known first order method to find a feasible solution to a conic problem is an adapted von Neumann algorithm. We improve the distance reduction step there by projecting onto the convex hull of previously generated points using a primal…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…
In this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the…
We examine the problem of projecting subsets of a commutative, positively ordered monoid into an $o$-ideal. We prove that to this end one may restrict to a sufficient subset, for whose cardinality we provide an explicit upper bound. Several…
Recently wide application in engineering-economic problems was received with problems of vector optimization. Development of methods of the decision of these problems it is executed in works A. Messac and others. Complexity of the offered…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
Nonlinear polynomial selection algorithms for the number field sieve address the problem of constructing polynomials with small coefficients by reducing to instances of the well-studied problem of finding short vectors in lattices. The…
We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…
We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting…
A large number matrix optimization problems are described by orthogonally invariant norms. This paper is devoted to the study of variational analysis of the orthogonally invariant norm cone of symmetric matrices. For a general orthogonally…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
We are presenting a simple and numerical stable algorithm for the solution of the cone projection problem which is suitable for relative small data sets and for simulation purposes needed for convexity tests. Not even one pseudo-inverse…
We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…