What is the e®ect of national antitrust policies in a world with international trade? Traditionally, economic analysis of mergers has assumed a closed economy, which as we show in this paper, may lead to errant policy in an open economy. We use a very simple model to highlight some key issues in optimal competition policy when trade is important, and compare the nationally optimal number of ̄rm...

In this paper, we propose a general smoothing Broyden-like quasi-Newton method for solving a class of nonsmooth equations. Under appropriate conditions, the proposed method converges to a solution of the equation globally and superlinearly. In particular, the proposed method provides the possibility of developing a quasi-Newton method that enjoys superlinear convergence even if strict complemen...

Existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient IS1 when an FIR equalizer is used. In this paper, we impose convexity on the cost function and anchoring of the equalizer away from the all-zero setup. We establish that there exists a globally convergent blind ...

We consider structural topology optimization problems including unilateral constraints arising from non-penetration conditions in contact mechanics. The resulting non-convex non-smooth problems are instances of mathematical programs with equilibrium constraints (MPEC), or bi-level programs. Applying nested (implicit programming) algorithms to this class of problems is problematic owing to the s...

We study the problem of minimizing the sum of a smooth strongly convex function and a non-smooth convex function. We consider solving this problem using the proximal gradient (PG) method, which at each iteration uses the proximal operator with respect to the non-smooth convex function at the intermediate iterate obtained using the gradient with respect to the smooth strongly convex function. We...

We present globally convergent incremental EM algorithms for reconstruction in emission tomography, COSEMML for maximum likelihood and COSEM-MAP for maximum a posteriori reconstruction. The COSEM (Complete data Ordered Subsets Expectation Maximization) algorithms use ordered subsets (OS) for fast convergence, but unlike other globally convergent OS-based ML and MAP algorithms such as RAMLA (Bro...

This paper examines the convergence properties of a class of learning schemes for concave N -person games – that is, games with convex action spaces and individually concave payoff functions. Specifically, we focus on a family of learning methods where players adjust their actions by taking small steps along their individual payoff gradients and then “mirror” the output back to their feasible a...