## A Trust-Region Algorithm for Global Optimization

We consider the global minimization of a bound-constrained function with a so-called funnel structure. We develop a two-phase procedure that uses sampling, local optimization, and Gaussian smoothing to construct a smooth model of the underlying funnel. The procedure is embedded in a trust-region framework that avoids the pitfalls of a fixed sampling radius. We present … Read more

## Adaptive Large Neighborhood Self-Regular Predictor-Corrector IPMs for LO

It is known that predictor-corrector methods in a large neighborhood of the central path are among the most efficient interior point methods (IPMs) for linear optimization (LO) problems. The best iteration bound based on the classical logarithmic barrier function is $O\left(n\log{\frac{n}{\epsilon}}\right)$. In this paper we propose a family of self-regular proximity based predictor-corrector (SR-PC) IPM … Read more

## Stochastic Programming with Equilibrium Constraints

In this paper we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We also discuss consistency and rates of convergence of sample average approximations of such stochastic problems. Citation School of Industrial … Read more

## Optimizing Call Center Staffing using Simulation and Analytic Center Cutting Plane Methods

We present a simulation-based analytic center cutting plane method to solve a sample average approximation of a call center problem of minimizing staffing costs, while maintaining an acceptable level of service in multiple time periods. We establish convergence of the method when the service level functions are discrete pseudoconcave. An extensive numerical study of a … Read more

## Dynamic Bundle Methods

Lagrangian relaxation is a popular technique to solve difficult optimization problems. However, the applicability of this technique depends on having a relatively low number of hard constraints to dualize. When there are many hard constraints, it may be preferable to relax them dynamically, according to some rule depending on which multipliers are active. From the … Read more

## Stochastic p-Robust Location Problems

Many objectives have been proposed for optimization under uncertainty. The typical stochastic programming objective of minimizing expected cost may yield solutions that are inexpensive in the long run but perform poorly under certain realizations of the random data. On the other hand, the typical robust optimization objective of minimizing maximum cost or regret tends to … Read more

## Security-constrained transmission planning: A mixed-integer disjunctive approach

We extend a static mixed intger diajunctive (MID) transmission expansion planning model so as to deal with circuit contingency criterion. The model simultaneously represents the network constraints for base case and each selected circuit contingency. The MID approach aloows a commercial optimization solver to achieve and prove solution aptimiality. The proposed approach is applied to … Read more

## OPTIMIZATION-BASED SIMULATION OF NONSMOOTH RIGID MULTIBODY DYNAMICS

We present a time-stepping method to simulate rigid multibody dynamics with inelastic collision, contact, and friction. The method progresses with ﬁxed time step without backtracking for collision and solves at every step a strictly convex quadratic program. We prove that a solution sequence of the method converges to the solution of a measure diﬀerential inclusion. … Read more

## ON USING THE ELASTIC MODE IN NONLINEAR PROGRAMMING APPROACHES TO MATHEMATICALPROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sucient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and that satisfy the quadratic growth condition can … Read more

## GLOBAL CONVERGENCE OF AN ELASTIC MODE APPROACH FOR A CLASS OF MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

We prove that any accumulation point of an elastic mode approach, applied to the optimization of a mixed P variational inequality, that approximately solves the relaxed subproblems is a C-stationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satis es the MPCC-LICQ constraint quali cation and if … Read more