In this paper we present the convergence analysis of the inexact infeasible path-following (IIPF) interior point algorithm. In this algorithm the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary...

A recently proposed trust-region approach for bound-constrained nonlinear equations is applied to the KKT systems arising from the discretization of a class of PDE-constrained optimization problems. Two different implementations are developed that take into account the large dimension and the special structure of the problems. The linear algebra phase is analyzed considering the possibility of ...

We consider the bilevel programming problem and its optimal value and KKT one level reformulations. The two reformulations are studied in a unified manner and compared in terms of optimal solutions, constraint qualifications and optimality conditions. We also show that any bilevel programming problem where the lower level problem is linear with respect to the lower level variable, is partially ...

ارتباط خداوند با انسان (و لوازم آن) همواره از مباحث مناقشه‌انگیز در میان الهی‌دانان بوده است. مهم‌ترین شعب این بحث، مسئلة «تغییرپذیری» پیناک (از بنیان‌گذاران الهیات گشوده) معتقد است آنجا که ـ بنا بر کتاب مقدس جهان و همچنین تدبیر متغیر منطقاً نیازمند مدبری بتواند شرایط مناسبی داشته باشد، ناگزیر باید موجودی تغییرپذیر باشد. مسئله کلام امامیه به گونه‌ای دیگر تبیین شده دیدگاه متکلمان اگرچه هر لحظه مخ...

1 The " convex " KKT theorem: a recapitulation We recall the Karush-Kuhn-Tucker theorem for convex programming, as treated in the previous lecture (see Corollary 3.5 of [OSC]).

We present the convergence analysis of the inexact infeasible pathfollowing (IIPF) interior-point algorithm. In this algorithm, the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary to study the ...

We discuss methods for solving the key linear equations within primal-dual barrier methods for linear and quadratic programming. Following Freund and Jarre, we explore methods for reducing the Newton equations to 2× 2 block systems (KKT systems) in a stable manner. Some methods require partitioning the variables into two or more parts, but a simpler approach is derived and recommended. To justi...