Zeta regularized determinants for conic manifolds

We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ-determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant.     

On circular–linear one-factorizations of the complete graph

In Korchmáros et al. (2018)one-factorizations of the complete graph $K_n$ are constructed for $n=q+1$ with any odd prime power $q$ such that either $q\equiv 1(mod4)$ or $q=2^h?1$. The arithmetic restriction $n=q+1$ is due to the fact that the vertices of $K_n$ in the construction are the points of a conic $\Omega$ in the finite plane of order $q$. Here we work on the Euclidean plane and describe an analogous construction where the role of $\Omega$ is taken by a regular $n$-gon. This allows us to remove the above constraints and construct one-factorizations of $K_n$ for every even $n\ge 6$.     

Shape controlled interpolatory ternary subdivision

Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support.In this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements. We show that both these features can be included in a unique interpolating 4-point subdivision method by means of non-stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes. This is realized by exploiting local shape parameters associated with the initial polyline edges.     

Numerical limit analysis bounds for ductile porous media with oblate voids

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by [Gologanu et al., 1994] and [Gologanu et al., 1997] for porous media with oblate voids.     

一类锥模型非单调信赖域算法及收敛性分析

本文对无约束优化问题提出了一类基于锥模型的非单调信赖域算法.二次模型非单调信赖域算法是新算法的特例.在适当的条件下,证明了算法的全局收敛性及Q-二次收敛性.     

Interior projection-like methods for monotone variational inequalities

We propose new interior projection type methods for solving monotone variational inequalities. The methods can be viewed as a natural extension of the extragradient and hyperplane projection algorithms, and are based on using non Euclidean projection-like maps. We prove global convergence results and establish rate of convergence estimates. The projection-like maps are given by analytical formulas for standard constraints such as box, simplex, and conic type constraints, and generate interior trajectories. We then demonstrate that within an appropriate primal-dual variational inequality framework, the proposed algorithms can be applied to general convex constraints resulting in methods which at each iteration entail only explicit formulas and do not require the solution of any convex optimization problem. As a consequence, the algorithms are easy to implement, with low computational cost, and naturally lead to decomposition schemes for problems with a separable structure. This is illustrated through examples for convex programming, convex-concave saddle point problems and semidefinite programming.The work of this author was partially supported by the United States–Israel Binational Science Foundation, BSF Grant No. 2002-2010.     

Blocking Sets of Certain Line Sets Related to a Conic

In this paper we classify point sets of minimum size of two types (1) point sets meeting all secants to an irreducible conic of the desarguesian projective plane PG(2,q), q odd; (2) point sets meeting all external lines and tangents to a given irreducible conic of the desarguesian projective plane PG(2,q), q even.     

Conic mixed-integer rounding cuts

A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that solve either second-order conic programming or linear programming relaxations of conic integer programs at the nodes of the branch-and-bound tree. Central to our approach is a reformulation of the second-order conic constraints with polyhedral second-order conic constraints in a higher dimensional space. In this representation the cuts we develop are linear, even though they are nonlinear in the original space of variables. This feature leads to a computationally efficient implementation of nonlinear cuts for conic mixed-integer programming. The reformulation also allows the use of polyhedral methods for conic integer programming. We report computational results on solving unstructured second-order conic mixed-integer problems as well as mean–variance capital budgeting problems and least-squares estimation problems with binary inputs. Our computational experiments show that conic mixed-integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed-integer programs and, hence, improving their solvability. This research has been supported, in part, by Grant # DMI0700203 from the National Science Foundation.