We point out an omission in the paper ‘The Algebraic Structure of the Arbitrary-Order Cone’ by Alzalg published in J. Optim. Theory Appl. in 2016. In reaction to this omission, some alternative results have been presented. Article Download View A Comment on the Paper `The Algebraic Structure of the Arbitrary-Order Cone'
We propose a randomized gradient method – or a randomized cutting-plane method from a dual viewpoint. From the primal viewpoint, our method bears a resemblance to the stochastic approximation family. But in contrast to stochastic approximation, the present method builds a model problem. Citation Kecskemet College, Pallasz Athene University. Izsaki ut 10, 6000 Kecskemet, Hungary; … Read more
Scenarios are indispensable ingredients for the numerical solution of stochastic optimization problems. Earlier approaches for optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based on distances containing minimal information, i.e., on data appearing … Read more
In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and specific directions (that we name active-set gradient related directions) satisfying a new … Read more
We develop polynomial-time heuristic methods to solve unimodular quadratic programs (UQPs) approximately, which are known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present three … Read more
Direct search methods are mainly designed for use in problems with no equality constraints. However, there are many instances where the feasible set is of measure zero in the ambient space and no mesh point lies within it. There are methods for working with feasible sets that are (Riemannian) manifolds, but not all manifolds are … Read more
The proximal ADMM which adds proximal regularizations to ADMM’s subproblems is a popular and useful method for linearly constrained separable convex problems, especially its linearized case. A well-known requirement on guaranteeing the convergence of the method in the literature is that the proximal regularization must be positive semidefinite. Recently it was shown by He et … Read more
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite non-convexities in the feasible region. As a side result, we present a new characterization of the conflict separation condition in the form of … Read more
For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric Gauss-Seidel (block sGS) method exactly solves the associated quadratic programming (QP) problem but added with an … Read more
We consider a Procrustes matching problem for non-negative matrices that arose in random tomography. As an alternative to the Frobenius distance, we propose an alternative non-symmetric distance using generalized inverses. Among its advantages is that it leads to a relatively simple quadratic function that can be optimized with least-square methods on manifolds. Citation Accepted for … Read more