This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond ex...

We investigate the problem of estimating a random variable Y ∈ Y under a privacy constraint dictated by another correlated random variable X ∈ X , where estimation efficiency and privacy are assessed in terms of two different loss functions. In the discrete case, we use the Hamming loss function and express the corresponding utility-privacy tradeoff in terms of the privacy-constrained guessing ...

Maximum-a-Posteriori (MAP) inference lies at the heart of Graphical Models and Structured Prediction. Despite the intractability of exact MAP inference, approximate methods based on LP relaxations have exhibited superior performance across a wide range of applications. Yet for problems involving large output domains (i.e., the state space for each variable is large), standard LP relaxations can...

The material properties of greatest importance in microwave processing of a dielectric are the complex relative permittivity ε = ε′ jε′′, and the loss tangent, tan δ = ε′′/ ε′. The real part of the permittivity, ε′, sometimes called the dielectric constant, mostly determines how much of the incident energy is reflected at the air-sample interface, and how much enters the sample. This paper show...

Frictional contact is one of the most challenging problems in computational mechanics. Typically, it a tough nonlinear problem often requiring several Newton iterations to converge and causing troubles also solution related linear systems. When modeled with aid Lagrange multipliers, impenetrability condition enforced exactly, but associated Jacobian matrix indefinite needs special treatment for...

In this paper, we propose an uniformly convergent adaptive finite element method with hybrid basis (AFEM-HB) for the discretization of singularly perturbed nonlinear eigenvalue problems under constraints with applications in Bose-Einstein condensation (BEC) and quantum chemistry. We begin with the time-independent Gross-Pitaevskii equation and show how to reformulate it into a singularly pertur...

We introduce a filter mechanism to force convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows fo...

Given a finite set of m scenarios, computing a portfolio with the minimium Value-at-Risk (VaR) is computationally difficult: the portfolio VaR function is non-convex, non-smooth, and has many local minima. Instead of formulating an n-asset optimal VaR portfolio problem as minimizing a loss quantile function to determine the asset holding vector R, we consider it as a minimization problem in an ...

The synthetic control method (SCM) is a popular approach for estimating the impact of treatment on single unit in panel data settings. “synthetic control” weighted average units that balances treated unit’s pretreatment outcomes and other covariates as closely possible. A critical feature original proposal to use SCM only when fit excellent. We propose Augmented an extension settings where such...