This paper studies the relationship between the so-called bi-quadratic optimization problem and its semidefinite programming (SDP) relaxation. It is shown that each r -bound approximation solution of the relaxed bi-linear SDP can be used to generate in randomized polynomial time an O(r)-approximation solution of the original bi-quadratic optimization problem, where the constant in O(r) does not...

This paper presents stability analysis and robust H∞ control for nonlinear switched systems bounded in sectors with arbitrary boundaries. By proposing new and more general multiple Lyapunov functions that incorporate nonlinearities in the system, we formulate the stability conditions under arbitrary switching in the form of linear matrix inequalities. Moreover, an optimization problem subject t...

In this paper, a bi-objective mixed-integer linear optimization model for Closed-loop Supply Chain Network Design Problem (CLSCND) is developed. The proposed model includes both the forward and reverse directions and includes different types of facilities, namely, manufacturing/remanufacturing centers, warehouses, and disassembly centers. The first objective function tried to minimize the total...

In this paper, a new version of multi-objective differential evolution with dynamically adaptable mutation factor is used for Pareto optimization of a 5-degree of freedom vehicle vibration model excited by non-stationary random road profile. In this way, non-dominated sorting algorithm and crowding distance criterion have been combined to differential evolution with fuzzified mutation in order ...

Offline inter-domain outbound Traffic Engineering (TE) can be formulated as an optimization problem whose objective is to determine primary egress points for traffic exiting a domain. However, when egress point failures happen, congestion may occur if secondary egress points are not carefully determined. In this paper, we formulate a bi-level outbound TE problem in order to make outbound route ...

We develop optimization models to analyze the demand for financial assets by heterogeneous agents. The models extend Frankel’s (1985) earlier approach, and relax the assumption of normality of asset returns. We assume, instead, that investors maximize an expected utility of terminal wealth based on heterogeneous attitudes toward risk. Solving a bi-level optimization program we endogenously esti...

We consider a nonlinear optimization problem governed by partial differential equations (PDE) with uncertain parameters. It is addressed by a robust worst case formulation. The resulting optimization problem is of bi-level structure and is difficult to treat numerically. We propose an approximate robust formulation that employs linear and quadratic approximations. To speed up the computation, r...

We present an automated methodology to optimize laminated composite structures. Our approach, inspired by bi-level optimization scheme, avoids its prime deficiencies and is based on developed computationally inexpensive stacking sequences reconstruction algorithm, which identically satisfies conventional set of blending rules. We combine it with proposed tight approximation to feasible domain o...

With rapid technological innovation and strong competition in hi-tech industries such as computer and communication organizations, the upstream component price and the downstream product cost usually decline significantly with time. As a result, an effective pricing supply chain model is very important. This paper first establishes two bi-level pricing models for pricing problems with the buyer...

Multi-label classification is a central problem in many application domains. In this paper, we present a novel supervised bi-directional model that learns a low-dimensional mid-level representation for multilabel classification. Unlike traditional multi-label learning methods which identify intermediate representations from either the input space or the output space but not both, the mid-level ...