In a recent work [3] the authors improved one of the most efficient interior-point approaches for some classes of block-angular problems. This was achieved by adding a quadratic regularization to the logarithmic barrier. This regularized barrier was shown to be self-concordant, thus fitting the general structural optimization interior-point framework. In practice, however, most codes implement ...

We observe a curious property of dual versus primal-dual path-following interior-point methods when applied to unbounded linear or conic programming problems in dual form. While primal-dual methods can be viewed as implicitly following a central path to detect primal infeasibility and dual unboundedness, dual methods can sometimes implicitly move away from the analytic center of the set of infe...

Dual-primal FETI methods for linear elasticity problems in three dimensions are considered. These are nonoverlapping domain decomposition methods where some primal continuity constraints across subdomain boundaries are required to hold throughout the iterations, whereas most of the constraints are enforced by Lagrange multipliers. An algorithmic framework for dualprimal FETI methods is describe...

A primal index of productivity change is introduced which decomposes exactly in three components: technical change, technical efficiency change and average scale economies (radial scale change). The proposed index is invariant to movement along indifference surfaces and it collapses to the Malmquist index if the technology is locally constant returns to scale. It is the best linear approximatio...

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions...

This paper presents two recurrent neural networks for solving the shortest path problem. Simplifying the architecture of a recurrent neural network based on the primal problem formulation, the first recurrent neural network called the primal routing network has less complex connectivity than its predecessor. Based on the dual problem formulation, the second recurrent neural network called the d...

In this paper, for handling general minimum-effort inverse-kinematic problems, the nonuniqueness condition is investigated. A set of nonlinear equations and inequality is presented for online nonuniqueness-checking. The concept and utility of primal neural networks (NNs) are introduced in this context of dynamical inequalities and constraints. The proposed primal NN can handle well such a nonli...