Approximate Dynamic Programming for Crowd-shipping with In-store Customers

Crowd-shipping has gained significant attention as a last-mile delivery option over the recent years. In this study, we propose a variant of dynamic crowd-shipping model with in-store customers as crowd-shippers to deliver online orders within few hours. We formulate the problem as a Markov decision process and develop an approximate dynamic programming (ADP) policy using … Read more

Applications of stochastic mixed-integer second-order cone optimization

Second-order cone programming problems are a tractable subclass of convex optimization problems and there are known polynomial algorithms for solving them. Stochastic second-order cone programming problems have also been studied in the past decade and efficient algorithms for solving them exist. A new class of interest to optimization community and practitioners is the mixed-integer version … Read more

Log-domain interior-point methods for convex quadratic programming

Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these conditions in the log-domain is a natural variation on this approach that to our knowledge is previously unstudied. In this paper, we analyze log-domain interior-point methods and prove their polynomial-time convergence. We also prove that they … Read more

Optimal error bounds in the absence of constraint qualifications with applications to the p-cones and beyond

We prove tight Hölderian error bounds for all p-cones. Surprisingly, the exponents differ in several ways from those that have been previously conjectured; moreover, they illuminate p-cones as a curious example of a class of objects that possess properties in 3 dimensions that they do not in 4 or more. Using our error bounds, we … Read more

Adaptive Sampling Quasi-Newton Methods for Zeroth-Order Stochastic Optimization

We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We develop modified versions of a norm … Read more

EETTlib – Energy-Efficient Train Timetabling Library

We introduce EETTlib, an instance library for the Energy-Efficient Train Timetabling problem. The task in this problem is to adjust a given timetable draft such that several key indicators relating to the energy consumption of the resulting railway traffic are minimized. These include peak power consumption, total energy consumption, loss in recuperation energy, fluctuation in … Read more

Scalable Parallel Nonlinear Optimization with PyNumero and Parapint

We describe PyNumero, an open-source, object-oriented programming framework in Python that supports rapid development of performant parallel algorithms for structured nonlinear programming problems (NLP’s) using the Message Passing Interface (MPI). PyNumero provides three fundamental building blocks for developing NLP algorithms: a fast interface for calculating first and second derivatives with the AMPL Solver Library (ASL), … Read more

A Local MM Subspace Method for Solving Constrained Variational Problems in Image Recovery

This article introduces a new Penalized Majorization-Minimization Subspace algorithm (P-MMS) for solving smooth, constrained optimization problems. In short, our approach consists of embedding a subspace algorithm in an inexact exterior penalty procedure. The subspace strategy, combined with a Majoration-Minimization step-size search, takes great advantage of the smoothness of the penalized cost function, while the penalty … Read more

The multiphase course timetabling problem

This paper introduces the multiphase course timetabling problem and presents mathematical formulations and effective solution algorithms to solve it in a real case study. Consider a pool of lessons and a number of students who are required to take a subset of these lessons to graduate. Each lesson consists of a predetermined and consecutive sequence … Read more

A quasi-Newton method with Wolfe line searches for multiobjective optimization

We propose a BFGS method with Wolfe line searches for unconstrained multiobjective optimization problems. The algorithm is well defined even for general nonconvex problems. Global convergence and R-linear convergence to a Pareto optimal point are established for strongly convex problems. In the local convergence analysis, if the objective functions are locally strongly convex with Lipschitz … Read more