We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of number of iterations, where L is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton's method.
We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter which defines the size of the neighborhood of the central-path and of the parameter which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined and converges...
In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinear program when the set Λ* of the Karush-Kuhn-Tucker multiplier vectors is empty owing to the fact that the constraint qualifications are not satisfied.
In this paper, we first present a polynomial-time primal-dual interior-point method (IPM) for solving linear programming (LP) problems, based on a new kernel function (KF) with a hyperbolic-logarithmic barrier term. To improve the iteration bound, we propose a parameterized version of this function. We show that the complexity result meets the currently best iteration bound for large-update methods by choosing a special value of the parameter. Numerical experiments reveal that the new KFs have better...
The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties....
In this paper we propose a primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main step of the algorithm consists of a feasibility step and several centering steps. At each iteration, we use only full-Newton step. Moreover, we use a more natural feasibility step, which targets at the -center. The iteration bound of the algorithm coincides...
In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.
Se presenta una implementación de un algoritmo primal-dual de punto interior para la solución de problemas lineales. El algoritmo difiere de otros ya existentes (como el implementado en el sistema LoQo) en el hecho de que soluciona las denominadas "ecuaciones normales en forma primal" (LoQo soluciona el denominado "sistema aumentado") y en que realiza una clara distinción entre variables acotadas superior e inferiormente, y aquéllas sólo acotadas inferiormente. La eficiencia de la implementación...
Les méthodes de points intérieurs en programmation linéaire connaissent un grand succès depuis l’introduction de l’algorithme de Karmarkar. La convergence de l’algorithme repose sur une fonction potentielle qui, sous sa forme multiplicative, fait apparaître un exposant . Cet exposant est, de façon générale, choisi supérieur au nombre de variables du problème. Nous montrons dans cet article que l’on peut utiliser des valeurs de plus petites que . Ceci permet d’améliorer le conditionnement de...
Les méthodes de points intérieurs en programmation linéaire connaissent un grand succès depuis l'introduction de l'algorithme de Karmarkar. La convergence de l'algorithme repose sur une fonction potentielle qui, sous sa forme multiplicative, fait apparaître un exposant p. Cet exposant est, de façon générale, choisi supérieur au nombre de variables n du problème. Nous montrons dans cet article que l'on peut utiliser des valeurs de p plus petites que n. Ceci permet d'améliorer le conditionnement...
We describe the solution of a bound constrained convex quadratic problem with limited memory resources. The problem arises from physical simulations occurring within video games. The motivating problem is outlined, along with a simple interior point approach for its solution. Various linear algebra issues arising in the implementation are explored, including preconditioning, ordering and a number of ways of solving an equivalent augmented system. Alternative approaches are briefly surveyed, ...
Atmospheric flow equations govern the time evolution of chemical concentrations in the atmosphere. When considering gas and particle phases, the underlying partial differential equations involve advection and diffusion operators, coagulation effects, and evaporation and condensation phenomena between the aerosol particles and the gas phase. Operator splitting techniques are generally used in global air quality models. When considering organic aerosol...