Abstract A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or nonlinear matrix-inequality constraint of the problem. We classify the sparsity in two types, the...

In this work we study the variational inequality problem in finite dimensional spaces. The constraint set we consider has the structure of semi-infinite programming. Standard convergence analysis for outer approximation methods includes boundedness of the constraint set, or, alternatively, coerciveness of the data. Using recession tools, we are able to replace these assumptions by the hypothese...

An inequality g{x) 2i 0 is often said to be a reverse convex constraint if the function g is continuous and convex. The feasible regions for linear program with an additional reverse convex constraint are generally non-convex and disconnected. In this paper a convergent algorithm for solving such a linear problem is proposed. The method is based upon a combination of the branch and bound proced...

In this paper, we consider a simple bilevel program where the lower level program is a nonconvex minimization problem with a convex set constraint and the upper level program has a convex set constraint. By using the value function of the lower level program, we reformulate the bilevel program as a single level optimization problem with a nonsmooth inequality constraint and a convex set constra...

This paper studies stability of error bounds for convex constraint systems in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems are considered.

In this article, I will consider Markov Decision Processes with two criteria, each defined as the expected value of an infinite horizon cumulative return. The second criterion is either itself subject to an inequality constraint, or there is maximum allowable probability that the single returns violate the constraint. I describe and discuss three new reinforcement learning approaches for solvin...

New iterative methods for solving systems of linear inequalities are presented. Each step in these methods consists of finding the orthogonat projection of the current point onto a hyperplane corresponding to a surrogate constraint which is constructed through a positive combination of a group of violated constraints. Both sequential and parallel-implementations are discussed.

● The weak inequality simply means that each factor is either (a) fully employed or (b) not fully employed. In this case, there are two unknown outputs but there are three (equality or inequality) constraints. ● It is necessary to have two independent equations in order to determine two unknown variables uniquely. ⇒ One of the constraints is redundant, i.e., that resource will not be fully empl...

Using new household survey data for 1995 and 2002, we investigate the size of China’s urban-rural income gap, the gap’s contribution to overall inequality in China, and the factors underlying the gap. Our analysis improves on past estimates by using a fuller measure of income, adjusting for spatial price differences and including migrants. Our methods include inequality decomposition by populat...

We conduct a systematic empirical study of cross-sectional inequality in the United States, integrating data from the Current Population Survey, the Panel Study of Income Dynamics, the Consumer Expenditure Survey, and the Survey of Consumer Finances. In order to understand how different dimensions of inequality are related via choices, markets, and institutions, we follow the mapping suggested ...