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In this paper we consider a mathematical program with semidefinite cone complementarity constraints (SDCMPCC). Such a problem is a matrix analogue of the mathematical program with (vector) complementarity constraints (MPCC) and includes MPCC as a special case. We first derive explicit formulas for the proximal and limiting normal cone of the graph of the(More)
In this paper, we define a class of linear conic programming (which we call matrix cone programming or MCP) involving the epigraphs of five commonly used matrix norms and the well studied symmetric cone. MCP has recently found many important applications, for example, in nuclear norm relaxations of affine rank minimization problems. In order to make the(More)
In this paper, we conduct a thorough study on the first and second order properties of the Moreau-Yosida regularization of the vector k-norm function, the indicator function of its epigraph, and the indicator function of the vector k-norm ball. We start with settling the vector k-norm case via applying the existing breakpoint searching algorithms to the(More)
Scissor structure is used to generate deployable objects for space-saving in a variety of applications, from architecture to aerospace science. While deployment from a small, regular shape to a larger one is easy to design, we focus on a more challenging task: designing a planar scissor structure that deploys from a given source shape into a specific target(More)
The reflection shapes of configurations in IR m with k landmarks consist of all the geometric information that is invariant under compositions of similarity and reflection transformations. By considering the corresponding Schoenberg embedding, we embed the reflection shape space into the Euclidean space of all (k − 1) by (k − 1) real symmetric matrices. In(More)
As 3D technology, including computer graphics, virtual reality and 3D printing, has been rapidly developed in the past years, 3D models are gaining an increasingly huge demand. Traditional 3D modeling platforms such as Maya and ZBrush, utilize “windows, icons, menus, pointers” (WIMP) interface paradigms for fine-grained control to construct detailed models.(More)