We propose a relaxation scheme for mathematical programs with equilibrium constraints (MPECs). In contrast to previous approaches, our relaxation is two-sided: both the complementarity and the nonnegativity constraints are relaxed. The proposed relaxation update rule guarantees (under certain conditions) that the sequence of relaxed subproblems will maintain a strictly feasible interior—even in...

An optimal control problem governed by an elliptic variational inequality is studied. The feasible set of the problem is relaxed and a pathfollowing type method is used to regularize the constraint on the state variable. First order optimality conditions for the relaxed-regularized subproblems are derived and convergence of stationary points with respect to the relaxation and regularization par...

We propose a relaxed correspondence assumption for cross-lingual projection of constituent syntax, which allows a supposed constituent of the target sentence to correspond to an unrestricted treelet in the source parse. Such a relaxed assumption fundamentally tolerates the syntactic non-isomorphism between languages, and enables us to learn the target-language-specific syntactic idiosyncrasy ra...

In this paper, we present a novel semidefinite programming approach for multiple-instance learning. We first formulate the multipleinstance learning as a combinatorial maximummargin optimization problem with additional instance selection constraints within the framework of support vector machines. Although solving this primal problem requires non-convex programming, we nevertheless can then der...

We investigate an alterative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy [1]. First, we directly demonstrate that the problem, which minimizes the recieved noise, interference, and clutter power under a minimum variance distortionless response (MVDR) constraint, is generally non-convex and provide concrete insight into the nature of th...

steel corrosion of bars in concrete structures is a complex process which leads to the reduction of the cross-section bars and decreasing the resistance of the concrete and steel materials. in this study, reliability analysis of a reinforced concrete beam with corrosion defects under the distributed load was investigated using the enhanced hasofer-lind and rackwitz-fiessler (ehl-rf) method base...

An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The f...

—This paper studies the two-hop co-located transmission architecture that incorporates simultaneous wireless information and power transfer in radio relay networks. Joint robust precoding design of the information and power transfer that can minimize the overall relays’ power consumption while satisfying our predefined quality-of-service and energy-harvest requirements is provided. By using Se...

The technique of relaxed power series expansion provides an efficient way to solve equations of the form F =Φ(F ), where the unknown F is a vector of power series, and where the solution can be obtained as the limit of the sequence 0,Φ(0),Φ(Φ(0)), . With respect to other techniques, such as Newton’s method, two major advantages are its generality and the fact that it takes advantage of possible...

We propose an integer linear programming (ILP) formulation for the minimum relay break point set (BPS) computation. Subsequently, in the ILP framework, we propose an alternate maximum-independent relay BPS formulation with the intention of minimizing dependency within the BPS. We show that 1) in practice, the relaxed version of the ILP suffices to obtain an integral vertex and 2) the relaxed ve...