Optimization and Systems Theory CHARACTERIZATION OF THE LIMIT POINT OF THE CENTRAL PATH IN SEMIDEFINITE PROGRAMMING
نویسندگان
چکیده
In linear programming, the central path is known to converge to the analytic center of the set of optimal solutions. Recently, it has been shown that this is not necessarily true for linear semidefinite programming in the absence of strict complementarity. The present paper deals with the formulation of a convex problem whose solution defines the limit point of the central path. This problem is closely related to the analytic center problem for the set of optimal solutions. In the strict complementarity case the problems are shown to coincide.
منابع مشابه
A path following interior-point algorithm for semidefinite optimization problem based on new kernel function
In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...
متن کاملA path-following infeasible interior-point algorithm for semidefinite programming
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...
متن کاملLimiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming
This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming obtained from centrality equations of the form XS + SX = 2νW , where W is a fixed positive definite matrix and ν > 0 is a parameter, under the assumption that the problem has a strictly complementary primal–dual optimal solution. We present a different and simpler proof than the one given ...
متن کاملA Recurrent Neural Network Model for Solving Linear Semidefinite Programming
In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...
متن کاملDynamical System Characterization of the Central Path and Its Variants - A Revisit
The notion of central path plays a fundamental role in the development of interior point methods which, in turn, have become important tools for solving various optimization problems. The central path equation is algebraic in nature and is derived from the KKT optimality conditions of a certain logarithmic barrier problem; meanwhile, the primal variable portion of the very same central path can...
متن کامل