Duality results on countably infinite linear programs are scarce. Subspaces that admit an interior point, which is a sufficient condition for a zero duality gap, yield a dual where the constraints cannot be expressed using the ordinary transpose of the primal constraint matrix. Subspaces that permit a dual with this transpose do not admit an interior point. This difficulty has stumped researche...

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

This paper analyzes local convergence rates of primal-dual interior point methods for general nonlinearly constrained optimization problems. For this purpose, we first discuss modified Newton methods and modified quasi-Newton methods for solving a nonlinear system of equations, and show local and Qquadratic/Q-superlinear convergence of these methods. These methods are characterized by a perturb...

This paper proposes two sets of rules Rule G and Rule P for controlling step lengths in a generic primal dual interior point method for solving the linear program ming problem in standard form and its dual Theoretically Rule G ensures the global convergence while Rule P which is a special case of Rule G ensures the O nL iteration polynomial time computational complexity Both rules depend only o...

We propose a polynomial time primal dual potential reduction algorithm for linear pro gramming The algorithm generates sequences d and v rather than a primal dual interior point xk sk where di q xi s k i and v k i q xi s k i for i n Only one element of d is changed in each iteration so that the work per iteration is bounded by O mn us ing rank one updating techniques The usual primal dual itera...

Constraint-reduction schemes have been proposed for the solution by interior-point methods of linear programs with many more inequality constraints than variables in standard dual form. Such schemes have been shown to be provably convergent and highly efficient in practice. A critical requirement of these schemes is the availability of an initial dual-feasible point. In this paper, building on ...

A new initialization or ‘Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path — our initial method (Algo...

Exploring Complexity of Large Update Interior-Point Methods for ) k ( P* Linear Complementarity Problems Based on Kernel Function KEYVAN AMINI* M.REZA PEYGHAMI +,2 ∗ Department of Sciences, Razi University, Kermanshah, Iran + Department of Sciences, Khajeh Nasir Toosi (KNT) University of Technology, Tehran, Iran Abstract. Interior Point Methods not only are the most effective methods in practic...

Duality theory is pervasive in finite dimensional optimization. There is growing interest in solving infinite-dimensional optimization problems and hence a corresponding interest in duality theory in infinite dimensions. Unfortunately, many of the intuitions and interpretations common to finite dimensions do not extend to infinite dimensions. In finite dimensions, a dual solution is represented...