The DIRECT algorithm is a deterministic sampling method for bound constrained Lipschitz continuous optimization. We prove a subsequential convergence result for the DIRECT algorithm that quantifies some of the convergence observations in the literature. Our results apply to several variations on the original method, including one that will handle general constraints. We use techniques from … Read more
We study the continuous trajectories for solving monotone nonlinear mixed complementarity problems over symmetric cones. While the analysis in Faybusovich (1997) depends on the optimization theory of convex log-barrier functions, our approach is based on the paper of Monteiro and Pang (1998), where a vast set of conclusions concerning continuous trajectories is shown for monotone … Read more
In this paper we present optimization algorithms for image restoration based on the total variation (TV) minimization framework of L. Rudin, S. Osher and E. Fatemi (ROF). Our approach formulates TV minimization as a second-order cone program which is then solved by interior-point algorithms that are efficient both in practice (using nested dissection and domain … Read more
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. CitationSchool of Industrial and … Read more
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
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
Sensitivity analysis is one of the most nteresting and preoccupying areas in optimization. Many attempts are made to investigate the problem’s behavior when the input data changes. Usually variation occurs in the right hand side of the constraints and/or the objective function coefficients. Degeneracy of optimal solutions causes considerable difficulties in sensitivity analysis. In this … Read more
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
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
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