Parallelizing Subgradient Methods for the Lagrangian Dual in Stochastic Mixed-Integer Programming

The dual decomposition of stochastic mixed-integer programs can be solved by the projected subgradient algorithm. We show how to make this algorithm more amenable to parallelization in a master-worker model by describing two approaches, which can be combined in a natural way. The first approach partitions the scenarios into batches and makes separate use of subgradient information for each batch. The second approach drops the requirement that evaluation of function and subgradient information is synchronized across the scenarios. We provide convergence analysis of both methods. We also evaluate their performance on two families of problems from SIPLIB on a single server with 32 single-core worker processes, demonstrating that when the number of workers is high relative to the number of scenarios, these two approaches (and their synthesis) can significantly reduce running time.

The Cleaved Core

The evolutionary trajectory of capitalism has now rendered the household precarious, economically disadvantaged, and vulnerable to the whims of firms under the authoritarian grip of the wrangler. Stagnant living standards for the vast majority of households in the metropolitan core is evidence that most households have been reduced to peripatetic hustlers in order to survive. Job loss haunts many areas within the core. Worker protections have been reduced to a minimum, and political alienation is on the rise. The Brexit decision in the United Kingdom, the election of an angry outsider to the presidency of the United States, and the rise of right-wing parties in Europe signal the extent to which households have become marginalized and angry.

Tailoring Globalization to Reduce Global Poverty and Inequality: a Case Study of the U.S.-Cambodian Bilateral Textile Agreement

Globalization has done little to fight global poverty and inequality. Though some critics have used this fact to argue against global economic integration, this article explains that those in favor of a freer and fairer global trade and finance system must link that regime with labor rights in order to achieve a reduction in global poverty and a more equitable distribution of trade gains. Without this connection, today's most powerful economies will be tomorrow's least relevant markets, finding themselves subordinate on the global supply chain to countries who were once thought of as “lesser developed.” This result will not come from increased development from those countries. Instead, it will derive from the erosion of progress in leading markets initiated by enhanced competition from countries with lower relative standards of living. Simply put: without a mechanism to increase those standards in the poorest countries, the richest countries will find their own standards retrograded in order to remain competitive. Accordingly, legal architectures must link free trade and global finance with core worker rights—or else.