We propose an efficient computational method for linearly constrained quadratic optimization problems (QOPs) with complementarity constraints based on their Lagrangian and doubly nonnegative (DNN) relaxation and first-order algorithms. The simplified Lagrangian-CPP relaxation of such QOPs proposed by Arima, Kim, and Kojima in 2012 takes one of the simplest forms, an unconstrained conic linear o...

The augmented Lagrangian method is a popular method for solving linearly constrained convex minimization problem and has been used many applications. In recently, the accelerated version of augmented Lagrangian method was developed. The augmented Lagrangian method has the subproblem and dose not have the closed form solution in general. In this talk, we propose the inexact version of accelerate...

Manufacturing scheduling is an important but difficult task. Building on our previous success in developing optimization-based scheduling methods using Lagrangian relaxation for practical applications, this paper presents a novel Lagrangian relaxation neural network (LRNN) optimization techniques. The convergence of LRNN for separable convex programming problems is established. For separable in...

We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modifi...

The paper focuses on the convergence rate of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under a set of assumptions of sufficient conditions, including the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second order sufficient condition, we first study some properties of the augmented Lagrangian and then ...

Abstract: In this brief, a modification of Lagrangian networks given in (Xia Y., 2003) is presented. This modification improves the settling time of the convergence of Lagrangian networks to a stationary point; which is the optimal solution to the nonlinear convex programming problem with linear equality constraints. This is important because, in many real-time applications where Lagrangian net...

Sequences of generalized Lagrangian duals and their SOS (sums of squares of polynomials) relaxations for a POP (polynomial optimization problem) are introduced. Sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP usin...

We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is an information-theoretic extension of conventional fullrationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the opti...

For design optimization tasks, quite often a so-called one-shot approach is used. It augments the solution of the state equation with a suitable adjoint solver yielding approximate reduced derivatives that can be used in an optimization iteration to change the design. The coordination of these three iterative processes is well established when only the state equation is considered as equality c...