Asymptotic behavior of the central path for a special class of degenerate SDP problems

Categories Semi-definite Programming Tags , , , ,

This paper studies the asymptotic behavior of the central path $(X(\nu),S(\nu),y(\nu))$ as $\nu \downarrow 0$ for a class of degenerate semidefinite programming (SDP) problems, namely those that do not have strictly complementary primal-dual optimal solutions and whose “degenerate diagonal blocks” $X_{\cT}(\nu)$ and $S_{\cT}(\nu)$ of the central path are assumed to satisfy $\max\{ \|X_{\cT}(\nu)\|, \|S_{\cT}(\nu)\| \} … Read more

Approximating the Two-Level Facility Location Problem Via a Quasi-Greedy Approach

Categories Approximation Algorithms Tags , ,

We propose a {\em quasi-greedy} algorithm for approximating the classical uncapacitated $2$-level facility location problem ($2$-LFLP). Our algorithm, unlike the standard greedy algorithm, selects a sub-optimal candidate at each step. It also relates the minimization $2$-LFLP problem, in an interesting way, to the maximization version of the single level facility location problem. Another feature of … Read more

Modeling Robust and Reliable Supply Chains

Categories Applications - OR and Management Sciences, Supply Chain Management Tags ,

We present formulations for the strategic design of robust and reliable supply chains with long term contracting. The inability to deliver a supply part due to unexpected events in a complex supply chain can have a significant impact on the performance of a supply chain. Reliable and robust supply chains leverage cost and risk of … Read more

Shunting Minimal Rail Car Allocation

Categories (Mixed) Integer Linear Programming, Transportation

We consider the rail car management at industrial in-plant railroads. Demands for materials or empty cars are characterized by a track, a car type, and the desired quantity. If available, we assign cars from the stock, possibly substituting types, otherwise we rent additional cars. Transportation requests are fulfilled as a short sequence of pieces of … Read more

A hybrid heuristic for the P-median problem

Categories Combinatorial Optimization, Meta Heuristics Tags , , , , ,

Given N customers and a set F of M potential facilities, the P-median problem consists in finding a subset of F with P facilities such that the cost of serving all customers is minimized. This is a well-known NP-complete problem with important applications in location science and classification (clustering). We present a multistart hybrid heuristic … Read more

Faster Approximation Schemes for Fractional Multicommodity Flow Problems

Categories Network Optimization Tags

We present fully polynomial approximation schemes for concurrent multicommodity flow problems that run in time of minimal dependency on the number of commodities k. We show that by modifying the algorithms by Garg & Konemann and Fleischer we can reduce their running time to a logarithmic dependence on k, and essentially match the running time … Read more

On Semidefinite Programming Relaxations for the Satisfiability Problem

Categories Combinatorial Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

This paper is concerned with the analysis and comparison of semidefinite programming (SDP) relaxations for the satisfiability (SAT) problem. Our presentation is focussed on the special case of 3-SAT, but the ideas presented can in principle be extended to any instance of SAT specified by a set of boolean variables and a propositional formula in … Read more

Error bounds and limiting behavior of weighted paths associated with the SDP map ^{1/2}SX^{1/2}$

Categories Semi-definite Programming Tags , , , ,

This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming obtained from centrality equations of the form $X^{1/2}S X^{1/2} = \nu W$, where $W$ is a fixed positive definite matrix and $\nu>0$ is a parameter, under the assumption that the problem has a strictly complementary primal-dual optimal solution. It is shown … Read more

A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing

Categories Meta Heuristics, Network Optimization, Telecommunications Tags , , , , , ,

Intra-domain traffic engineering aims to make more efficient use of network resources within an autonomous system. Interior Gateway Protocols such as OSPF (Open Shortest Path First) and IS-IS (Intermediate System-Intermediate System) are commonly used to select the paths along which traffic is routed within an autonomous system. These routing protocols direct traffic based on link … Read more

Finding the projection of a point onto the intersection of convex sets via projections onto halfspaces

Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization Tags , , , ,

We present a modification of Dykstra’s algorithm which allows us to avoid projections onto general convex sets. Instead, we calculate projections onto either a halfspace or onto the intersection of two halfspaces. Convergence of the algorithm is established and special choices of the halfspaces are proposed. The option to project onto halfspaces instead of general … Read more