In the traditional framework, social welfare functions depend on the mean income and on the income inequality. An alternative illfare framework has been developed to take into account the disutility of unfavorable variables. The illfare level is assumed to increase with the inequality of the distribution. In some social and economic fields, such as those related to employment, health, education...

Given a set of corrupted data drawn from a union of multiple subspace, the subspace recovery problem is to segment the data into their respective subspace and to correct the possible noise simultaneously. Recently, it is discovered that the task can be characterized, both theoretically and numerically, by solving a matrix nuclear-norm and a `2,1-mixed norm involved convex minimization problems....

in this paper we study isotropic lagrangian submanifolds , in complex space forms . it is shown that they are either totally geodesic or minimal in the complex projective space , if . when , they are either totally geodesic or minimal in . we also give a classification of semi-parallel lagrangian h-umbilical submanifolds.

where f : Rn → R and g : Rn → Rp are nonlinear continuous functions and Ω = {x ∈ Rn : −∞ < l ≤ x ≤ u < ∞}. Problems with equality constraints, h(x) = 0, can be reformulated into the above form by converting into a couple of inequality constraints h(x)− β ≤ 0 and −h(x)− β ≤ 0, where β is a small positive relaxation parameter. Since we do not assume that the objective function f is convex, the pr...

Lagrangian methods are popular in solving continuous constrained optimization problems. In this paper, we address three important issues in applying Lagrangian methods to solve optimization problems with inequality constraints. First, we study methods to transform inequality constraints into equality constraints. An existing method, called the slack-variable method, adds a slack variable to eac...

We define a primal-dual algorithm model (SOLA) for inequality constrained optimization problems that generates a sequence converging to points satisfying the second order necessary conditions for optimality. This property can be enforced by combining the equivalence between the original constrained problem and the unconstrained minimization of an exact augmented Lagrangian function and the use ...

§0. Introduction §1. The Scheme-Theoretic Fourier Transform §2. Discrete Gaussians and Gauss Sums §3. Review of Degree Computations in [HAT] §4. The Fourier Transform of an Algebraic Theta Function: The Case of an Étale Lagrangian Subgroup §5. The Fourier Transform of an Algebraic Theta Function: The Case of a Lagrangian Subgroup with Nontrivial Multiplicative Part §6. Generic Properties of the...

In this note we consider an autonomous Tonelli Lagrangian L on a closed manifold M , that is, a C2 function L : TM −→ R such that L is fiberwise strictly convex and superlinear. Then the Euler-Lagrange equation associated with L defines a complete flow φt on TM . Define Minv to be the set of Φt-invariant, compactly supported, Borel probability measures on TM . Mather showed that the function (c...

In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The proposed IAL framework requires solving the augmented Lagrangian (AL) subproblem at each iteration less accurately than most of the exist...