This paper analyzes sequences generated by infeasible interior point methods. In convex and nonconvex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We also show ...

We present a computationally eeective approach to representing and reasoning about actions with many qualiications. The approach involves treating actions as qualiied not by speciic facts that may or may not hold when the action is executed, but instead as potentially qualiied by general constraints describing the domain being investigated. Speciically, we suggest that the result of the action ...

One of the most time consuming activities in new product development is associated with reliability assessment and qualification. This is defined as a process to verify whether the anticipated reliability is indeed achieved under actual life cycle loads for some specified length of time. Reliability assessment and qualification is usually accomplished by testing under accelerated loads to achie...

In this paper, we propose a solution to McCarthy’s qualification problem [lo] based on the notion of possible worlds [3, 61. We begin by noting that existing formal solutions to qualification seem to us to suffer from serious epistemological and computational difficulties. We present a formalization of action based on the notion of possible worlds, and show that our solution to the qualificatio...

Augmented Lagrangian methods with convergence to second-order stationary points in which any constraint can be penalized or carried out to the subproblems are considered in this work. The resolution of each subproblem can be done by any numerical algorithm able to return approximate second-order stationary points. The developed global convergence theory is stronger than the ones known for curre...

A new duality theory is developed for a class of stochastic programs in which the probability distribution is not necessarily discrete. This provides a new framework for problems which are not necessarily bounded, are not required to have relatively complete recourse, and do not satisfy the typical Slater condition of strict feasibility. These problems instead satisfy a different constraint qua...

A novel and interesting approach to infinite and infinitesimal numbers was recently proposed in a series of papers and a book by Y. Sergeyev. This novel numeral system is based on the use of a new infinite unit of measure (the number grossone, indicated by the numeral 1), the number of elements of the set, N, of natural numbers. Based on the use of 1, De Cosmis and De Leone [1] have then propos...

We introduce two new weaker Constraint Qualifications (CQs) for mathematical programs with equilibrium (or complementarity) constraints, MPEC for short. One of them is a tailored version of the constant rank of subspace component (CRSC) and the other is a relaxed version of the MPECNo Nonzero Abnormal Multiplier Constraint Qualification (MPEC-NNAMCQ). Both incorporate the exact set of gradients...

Mathematical programming methods have traditionally been used extensively in the analysis and design of elastic/plastic structures. However, some of the recent results from parametric nonlinear programming have not been fully exploited in mechanical applications, particularly those relating to the causes of singularities due to parametric variations. In this paper, we reexamine the phenomenon o...