A New Face Algorithm Using LU Factorization for Linear Programming

The unique feature of the face algorithm \cite{pan14} is that it moves from face to face, rather than from vertex to vertex as the simplex algorithm. It uses the orthogonal projection of the negative objective gradient on the related null space as its search direction. Nevertheless, the algorithm is based on QR factorization, which would … Read more

Failure Probability Constrained AC Optimal Power Flow

Despite cascading failures being the central cause of blackouts in power transmission systems, existing operational and planning decisions are made largely by ignoring their underlying cascade potential. This paper posits a reliability-aware AC Optimal Power Flow formulation that seeks to design a dispatch point which has a low operator-specified likelihood of triggering a cascade starting … Read more

Convergence Rate of an Inertial Extragradient Method for Strongly Pseudomonotone Equilibrium Problems in Hilbert Spaces

In this work, we establish the $R$-linear convergence rate of the inertial extragradient method for solving strongly pseudo-monotone equilibrium problems with a new self adaptive step-size. The linear convergence rate of the proposed methods is obtained without the prior knowledge of the Lipschitz-type constants of the bifunction. We also discuss the application of the obtained … Read more

Two decades of blackbox optimization applications

This work reviews blackbox optimization applications over the last twenty years, addressed using direct search optimization methods. Emphasis is placed on the Mesh Adaptive Direct Search (MADS) derivative-free optimization algorithm. The core of the document describes applications in three specific fields: Energy, materials science, and computational engineering design. Other applications in science and engineering as … Read more

Halting Time is Predictable for Large Models: A Universality Property and Average-case Analysis

Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in optimization. One difficulty is that the analysis can depend on the probability distribution of the inputs to the model. However, we show … Read more

Fleet Sizing and Allocation for On-demand Last-Mile Transportation Systems

The last-mile problem refers to the provision of travel service from the nearest public transportation node to home or other destination. Last-Mile Transportation Systems (LMTS), which have recently emerged, provide on-demand shared transportation. In this paper, we investigate the fleet sizing and allocation problem for the on-demand LMTS. Specifically, we consider the perspective of a … Read more

An approximation algorithm for multi-objective optimization problems using a box-coverage

For a continuous multi-objective optimization problem, it is usually not a practical approach to compute all its nondominated points because there are infinitely many of them. For this reason, a typical approach is to compute an approximation of the nondominated set. A common technique for this approach is to generate a polyhedron which contains the … Read more

Compact Integer Linear Programming Formulations for the Temporal Bin Packing Problem with Fire-Ups

In this article we examine a specific version of the temporal bin packing problem (TBPP) that occurs in job-to-server scheduling. The TBPP represents a generalization of the well-known bin packing problem (BPP) with respect to an additional time dimension, and it requires to find the minimum number of bins (servers) to accommodate a given list … Read more

Dynamic Discretization Discovery for Solving the Continuous Time Inventory Routing Problem with Out-and-Back Routes

In time dependent models, the objective is to find the optimal times (continuous) at which activities occur and resources are utilized. These models arise whenever a schedule of activities needs to be constructed. A common approach consists of discretizing the planning time and then restricting the decisions to those time points. However, this approach leads … Read more

An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone

A weakly infeasible semidefinite program (SDP) has no feasible solution, but it has nearly feasible solutions that approximate the constraint set to arbitrary precision. These SDPs are ill-posed and numerically often unsolvable. They are also closely related to “bad” linear projections that map the cone of positive semidefinite matrices to a nonclosed set. We describe … Read more