A Proximal Quasi-Newton Trust-Region Method for Nonsmooth Regularized Optimization

We develop a trust-region method for minimizing the sum of a smooth term f and a nonsmooth term h, both of which can be nonconvex. Each iteration of our method minimizes apossibly nonconvex model of f+h in a trust region. The model coincides with f+h in value and subdifferential at the center. We establish global … Read more

Optimizing Driver Menus Under Stochastic Selection Behavior for Ridesharing and Crowdsourced Delivery

Peer-to-peer logistics platforms coordinate independent drivers to fulfill requests for last mile delivery and ridesharing. To balance demand-side performance with driver autonomy, a new methodology is created to provide drivers with a small but personalized menu of requests to choose from. This creates a Stackelberg game, in which the platform leads by deciding what menu … Read more

Exact algorithms for the 0-1 Time-bomb Knapsack Problem

We consider a stochastic version of the 0–1 Knapsack Problem in which, in addition to profit and weight, each item is associated with a probability of exploding and destroying all the contents of the knapsack. The objective is to maximize the expected profit of the selected items. The resulting problem, denoted as 0–1 Time-Bomb Knapsack … Read more

Scalable adaptive cubic regularization methods

Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in performing an iterative search for the shift akin to solving the secular equation in trust-region methods. Such search requires computing the Cholesky factorization of … Read more

Decomposition strategies for vehicle routing heuristics

Decomposition techniques are an important component of modern heuristics for large instances of vehicle routing problems. The current literature lacks a characterisation of decomposition strategies and a systematic investigation of their impact when integrated into state-of-the-art heuristics. This paper fills this gap: we discuss the main characteristics of decomposition techniques in vehicle routing heuristics, highlight … Read more

Complexity of a Projected Newton-CG Method for Optimization with Bounds

This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate … Read more

Fast cluster detection in networks by first-order optimization

Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we … Read more

Assortment Optimization under the Decision Forest Model

The decision forest model is a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in particular, can be used to represent non-rational customer behavior. In this paper, we study the problem of finding the assortment that maximizes expected revenue under the decision forest model. This problem is of … Read more

Long-run market equilibria in coupled energy sectors: A study of uniqueness

We propose an equilibrium model for coupled markets of multiple energy sectors. The agents in our model are operators of sector-specific production and sector-coupling technologies, as well as price-sensitive consumers with varying demand. We analyze long-run investment in production capacity in each sector and investment in coupling capacity between sectors, as well as production decisions … Read more

Minimizing Nonsmooth Convex Functions with Variable Accuracy

We consider unconstrained optimization problems with nonsmooth and convex objective function in the form of mathematical expectation. The proposed method approximates the objective function with a sample average function by using different sample size in each iteration. The sample size is chosen in an adaptive manner based on the Inexact Restoration. The method uses line … Read more