نتایج جستجو برای: primal dual method

تعداد نتایج: 1767116  

Journal: :SIAM J. Scientific Computing 2003
James Lu David L. Darmofal

The adjoint solution has found many uses in computational simulations where the quantities of interest are the functionals of the solution, including design optimization, error estimation, and control. In those applications where both the solution and the adjoint are desired, the conventional approach is to apply iterative methods to solve the primal and dual problems separately. However, we sh...

2004
F. A. Potra

In this paper, we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate the error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions, the error bounds for the primal and dual sequences converge ...

1996
Jean-Philippe VIAL

We propose a generic path-following scheme which is essentially a method of centers that can be implemented with a variety of algorithms. The complexity estimate is computed on the sole assumption that a certain local quadratic convergence property holds, independently of the speciic algorithmic procedure in use, primal, dual or primal-dual. We show convergence in O(p n) iterations. We verify t...

Journal: :Math. Program. 2014
Thomas Davi Florian Jarre

The recent approach of solving large scale semidefinite programs with a first order method by minimizing an augmented primal-dual function is extended to doubly nonnegative programs. A key point governing the convergence of this approach are regularity properties of the underlying problem. Regularity of the augmented primal-dual function is established under the condition of uniqueness and stri...

Journal: :Applied Mathematics and Optimization 2023

Abstract The primal-dual method of Chambolle and Pock is a widely used algorithm to solve various optimization problems written as convex-concave saddle point problems. Each update step involves the application both forward linear operator its adjoint. However, in practical applications like computerized tomography, it often computationally favourable replace adjoint by more efficient approxima...

Journal: :SIAM Journal on Optimization 2000
Jean-Louis Goffin Jean-Philippe Vial

We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables within the trust regions defined by Dikin’s primal and dual ellipsoids. The new primal and dual dir...

Journal: :Journal of the Operations Research Society of Japan 1988

Journal: :Algorithmic Operations Research 2008
Igor Griva David F. Shanno Robert J. Vanderbei Hande Y. Benson

Many recent convergence results obtained for primal-dual interior-point methods for nonlinear programming, use assumptions of the boundedness of generated iterates. In this paper we replace such assumptions by new assumptions on the NLP problem, develop a modification of a primal-dual interior-point method implemented in software package loqo and analyze convergence of the new method from any i...

Journal: :Optimization Methods and Software 2009
Hiroshi Yamashita Hiroshi Yabe

In this paper, we are concerned with nonlinear minimization problems with second order cone constraints. A primal-dual interior point method is proposed for solving the problems. We also propose a new primal-dual merit function by combining the barrier penalty function and the potential function within the framework of the line search strategy, and show the global convergence property of our me...

2014
Valentin Nedelcu Ioan Dumitrache

We propose in this paper an inexact dual gradient algorithm based on augmented Lagrangian theory and inexact information for the values of dual function and its gradient. We study the computational complexity certification of the proposed method and we provide estimates on primal and dual suboptimality and also on primal infeasibility. We also discuss implementation aspects of the proposed algo...

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