One of the main drawbacks associated with Interior Point Methods (IPM) is the perceived lack of an efficient warmstarting scheme which would enable the use of information from a previous solution of a similar problem. Recently there has been renewed interest in the subject. A common problem with warmstarting for IPM is that an advanced starting point which is close to the boundary of the feasib...

Abstract We propose a method to reduce the sizes of SDP relaxation problems for a given polynomial optimization problem (POP). This method is an extension of the elimination method for a sparse SOS polynomial in [8] and exploits sparsity of polynomials involved in a given POP. In addition, we show that this method is a partial application of a facial reduction algorithm, which generates a small...

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step len...

Stability and performance are two main issues in motion of bipeds. To ensure stability of motion, a biped needs to follow specific pattern to comply with a stability criterion such as zero moment point. However, there are infinity many patterns of motion which ensure stability, so one might think of achieving better performance by choosing proper parameters of motion. Step length and step perio...

A large-step infeasible-interior-point method is proposed for solving P∗(κ)-matrix linear complementarity problems. It is new even for monotone LCP. The algorithm generates points in a large neighborhood of an infeasible central path. Each iteration requires only one matrix factorization. If the problem is solvable, then the algorithm converges from arbitrary positive starting points. The compu...

Optimization using the L∞ norm is an increasingly important area in multiview geometry. Previous work has shown that globally optimal solutions can be computed reliably using the formulation of generalized fractional programming, in which algorithms solve a sequence of convex problems independently to approximate the optimal L∞ norm error. We found the sequence of convex problems are highly rel...

A polynomial complexity bound is established for an interior point path following algorithm for the monotone linear complementarity problem that is based on the Chen{Harker{Kanzow smoothing techniques. The fundamental diierence with the Chen{Harker and Kanzow algorithms is the introduction of a rescaled Newton direction. The rescaling requires the iterates to remain in the interior of the posit...

Service level agreement (SLA) is a powerful tool to formalize the negotiation and agreement between the service provider and service seeker with the scope of service quality characteristics, compensations and tariffs. The service quality description is the main part of a SLA which can be characterized by the use of suitable and feasible quality of service (QoS) parameters. Determining suitable ...

Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplexmethod. But their computational complexities are exponential, which is not satisfactory for solving largescale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programmi...

We propose an adaptation of the Feasible Direction Interior Points Algorithm (FDIPA) J. Herskovits, for solving large-scale linear programs. At each step, solution two systems with same coefficient matrix is determined. This step involves a significant computational effort. Reducing time is, therefore, way to improve performance method. The be solved are associated definite positive symmetric m...