Let S be an orientable, finite type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on was first defined and topologized by the author. In this article, we give explicit description topology using coordinates. More precisely, given every point in space, find continuous coordinates quotient a suitable open neighborhood about subgroup ma...

This paper discusses an optimization-based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system, which is subjected to the static load. We deal with the three problems in mechanics sharing the common mathematical properties: (i) structures containing no-compression cables; (ii) frictionless contacts; (iii) elastic-plastic trusses...

This paper discusses an optimization-based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system, which is subjected to the static load. We deal with the three problems in mechanics sharing the common mathematical properties: (i) structures containing nocompression cables; (ii) frictionless contacts; and (iii) elastic–plastic trus...

We study the generalization of split and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split...

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms and functions. Further, iteratively propagating from node to node along edge, we prove that “regarding the neural graph without triangles, it is nearly convex ...