Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...

This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated singularity, multiplicities of blowup algebras and mixed volumes of polytopes.

Associated with the notion of the mixed Lp-affine surface area for multiple convex bodies for all real p (p 6= −n) which was introduced by Ye, et al. [D. Ye, B. Zhu, J. Zhou, arXiv, 2013 (2013), 38 pages], we define the concept of the mixed Lp-dual affine surface area for multiple star bodies for all real p (p 6= −n) and establish its monotonicity inequalities and cyclic inequalities. Besides, ...

We present the numerical analysis on the Poisson problem of two mixed Petrov-Galerkin finite volume schemes for équations in divergence form div c/?(ti, Vit) = ƒ. The first scheme, which has been introduced in [22], is a generalization in two dimensions of Keller's box-scheme. The second scheme is the dual of the first one, and is a cell-centered scheme for u and the flux <p. For the first sche...

We study the dual mixed finite element approximation of unilateral contact problems. Based on the dual mixed variational formulation with three unknowns (stress, displacement and the displacement on the contact boundary), the a priori error estimates have been established for both conforming and nonconforming finite element approximations. A Uzawa type iterative algorithm is developed to solve ...

A Mond–Weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated. Applying the separability and generalized F-convexity on the functions involved, weak, strong and converse duality theorems are established. Self duality theorem is proved. A close relationship between these variational problems and static symmetric dual minimax mixed integer mul...

Lipschitz condition is a natural notion of function regularity in this context, and the norm dual to the mixed Lipschitz space is a natural distance between measures. In this paper, we consider the tensor product of spaces equipped with tree metrics and give effective formulas for the mixed Lipschitz norm and its dual. We also show that these norms behave well when approximating an arbitrary me...

We present a Multi-Resolution Dual method based on an incremental octree-based refinement strategy. Our solution is able to generate multi-resolution surfaces from segmented volumetric data. It extends the Dual Marching Cubes algorithm over a generalized octree and guarantees that the produced surfaces are always manifold by introducing a new cell-based criterion for dual vertices generation. M...

Abstract Mixed matrix membranes (MMMs) have been widely developed as an attractive solution to overcome the drawbacks found in most polymer membranes, such permeability-selectivity trade-off and low physicochemical stability. Numerous fillers based on inorganic, organic, hybrid materials with various structures including porous or nonporous, two-dimensional three-dimensional, used. Demanded fur...