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...

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The effective domain of the value function is described by a modification of the concept of convex core. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The minimizers and generalized minimizers are explicitly d...

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...