Adjustable robust treatment-length optimization in radiation therapy

Traditionally, optimization of radiation therapy (RT) treatment plans has been done before the initiation of RT course, using population-wide estimates for patients’ response to therapy. However, recent technological advancements have enabled monitoring individual patient response during the RT course, in the form of biomarkers. Although biomarker data remains subject to substantial uncertainties, information extracted from … Read more

An exact algorithm for robust influence maximization

We propose a Branch-and-Cut algorithm for the robust influence maximization problem. The influence maximization problem aims to identify, in a social network, a set of given cardinality comprising actors that are able to influence the maximum number of other actors. We assume that the social network is given in the form of a graph with … Read more

Accelerated Symmetric ADMM and Its Applications in Signal Processing

The alternating direction method of multipliers (ADMM) were extensively investigated in the past decades for solving separable convex optimization problems. Fewer researchers focused on exploring its convergence properties for the nonconvex case although it performed surprisingly efficient. In this paper, we propose a symmetric ADMM based on different acceleration techniques for a family of potentially … Read more

Optimal K-Thresholding Algorithms for Sparse Optimization Problems

The simulations indicate that the existing hard thresholding technique independent of the residual function may cause a dramatic increase or numerical oscillation of the residual. This inherit drawback of the hard thresholding renders the traditional thresholding algorithms unstable and thus generally inefficient for solving practical sparse optimization problems. How to overcome this weakness and develop … Read more

Relating Single-Scenario Facets to the Convex Hull of the Extensive Form of a Stochastic Single-Node Flow Polytope

Stochastic mixed-integer programs (SMIPs) are a widely-used modeling paradigm for sequential decision making under uncertainty. One popular solution approach to solving SMIPs is to solve the so-called “extensive form” directly as a large-scale (deterministic) mixed-integer program. In this work, we consider the question of when a facet-defining inequality for the convex hull of a deterministic, … Read more

Feeder Routing for Air-to-Air Refueling Operations

We consider the problem of routing a fleet of feeders for civil air-to-air refueling operations. In the air-to-air refueling problem, a fixed set of cruisers requires refueling by a fleet of feeders at fixed locations and fixed points in time. A typical objective function is to minimize the fuel consumption or the total number of … Read more

Arc routing with electric vehicles: dynamic charging and speed-dependent energy consumption

Concerns about greenhouse gas emissions and government regulations foster the use of electric vehicles. Several recently published articles study the use of electric vehicles (EVs) in node-routing problems. In contrast, this article considers EVs in the context of arc routing while also addressing practically relevant aspects that have not been addressed sufficiently so far. These … Read more

Adaptive cubic regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization

Abstract. We consider the Adaptive Regularization with Cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynamically. The theoretical analysis of the proposed procedure is given. The key property of ARC framework, constituted by optimal worst-case function/derivative evaluation bounds for first- and second-order critical point, is … Read more

A Unified Approach to Mixed-Integer Optimization Problems With Logical Constraints

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal component analysis and sparse learning problems. These problems exhibit logical relationships between continuous and discrete variables, which are usually reformulated linearly … Read more

Single-Forward-Step Projective Splitting: Exploiting Cocoercivity

This work describes a new variant of projective splitting for monotone inclusions, in which cocoercive operators can be processed with a single forward step per iteration. This result establishes a symmetry between projective splitting algorithms, the classical forward backward splitting method (FB), and Tseng’s forward-backward-forward method (FBF). Another symmetry is that the new procedure allows … Read more