We present a method for constructing seamless parametrization surfaces of any genus, which can handle feasible cone configuration with type cones. The mapping is guaranteed to be locally injective, due careful construction simple domain boundary polygon. polygon’s complexity depends on the cones in field, and it independent mesh geometry. result small polygon that optimized prior interior mappi...

In this paper, we are concerned with the numerical solution of simplicial cone constrained convex quadratic optimization (SCQO) problems. A reformulation K.K.T optimality conditions SCQOs as an equivalent linear complementarity problem $\mathcal{P}$-matrix ($\mathcal{P}$-LCP) is considered. Then, a feasible full-Newton step interior-point algorithm (IPA) applied for solving SCQO via $\mathcal{P...

An algorithm for solving linear programming problems can be used as a subroutine in methods for more complicated problems. Such methods usually involve solving a sequence of related linear programming problems, where the solution to one linear program is close to the solution to the next, that is, it provides a warm start for the next linear program. The branch and cut method for solving intege...

In [4] the second author presented a new primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best known bound for infeasible interior-point algorithms. Each iteration consists of a step that restores the feasibility for an intermediate problem (the so-called feasibility step) and a few (usual) centering steps. No more than O(n...

We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT...

We present a target-following framework for semidefinite programming, which generalizes the target-following framework for linear programming. We use this framework to build weighted path-following interior-point algorithms of three distinct flavors: short-step, predictor-corrector, and large-update. These algorithms have worst-case iteration bounds that parallel their counterparts in linear pr...

This paper deals with a class of primal-dual interior-point algorithms for semideenite programming (SDP) which was recently introduced by Kojima, Shindoh and Hara 11]. These authors proposed a family of primal-dual search directions that generalizes the one used in algorithms for linear programming based on the scaling matrix X 1=2 S ?1=2. They study three primal-dual algorithms based on this f...

In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant-step operation and f -representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish ...

Many interior-point methods for linear programming are based on the properties of the logarithmic barrier function. After a preliminary discussion of the convergence of the (primal) projected Newton barrier method, three types of barrier method are analyzed. These methods may be categorized as primal, dual and primal-dual, and may be derived from the application of Newton’s method to different ...

In this paper we propose a new interior-point method, which is based on an extension of the ideas of self-scaled optimization to the general cases. We suggest using the primal correction process to find a scaling point. This point is used to compute a strictly feasible primal-dual pair by simple projection. Then, we define an affine-scaling direction and perform a prediction step. This is the o...