Constraint qualifications and strong global convergence properties of an augmented Lagrangian method on Riemannian manifolds

Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent developments from nonlinear programming to the context of optimization on Riemannian manifolds, including equality and inequality constraints. Many research have … Read more

Regularized methods via cubic subspace minimization for nonconvex optimization

Categories Nonlinear Optimization, Unconstrained Optimization

The main computational cost per iteration of adaptive cubic regularization methods for solving large-scale nonconvex problems is the computation of the step \(s_k\), which requires an approximate minimizer of the cubic model. We propose a new approach in which this minimizer is sought in a low dimensional subspace that, in contrast to classical approaches, is … Read more

Reformulation-Perspectification Technique for nonconvex optimization problems

Categories Global Optimization, Nonlinear Optimization Tags , , , ,

In this paper, we propose a new global optimization approach for solving nonconvex optimization problems in which the nonconvex components are sums of products of convex functions. A broad class of nonconvex problems can be formulated in this way, such as concave minimization problems, problems with difference of convex functions in the objective and constraints, … Read more

Playing Stackelberg security games in perfect formulations

Categories Applications - OR and Management Sciences, Game Theory, Network Optimization

Protecting critical infrastructure from intentional damage requires foreseeing the strategies of possible attackers. The problem faced by the defender of such infrastructure can be formulated as a Stackelberg security game. A defender must decide what specific targets to protect with limited resources, maximizing their expected utility (e.g., minimizing damage value) and considering that a second … Read more

Integrating Order-to-Delivery Time Sensitivity in E-Commerce Middle-Mile Consolidation Network Design

Categories Production and Logistics, Supply Chain Management, Transportation Tags , , ,

This paper proposes an approach that leverages data on customer purchasing sensitivity to quoted order-to-delivery times (ODTs) when designing middle-mile consolidation networks to maximize the profit of e-commerce retailers. Our approach integrates quoted ODT-dependent sales volume predictions into a new mixed-integer program (MIP) that simultaneously determines ODT quotes and a consolidation plan, characterized by the … Read more

Exploiting user-supplied Decompositions inside Heuristics

Categories Integer Programming Tags , , , ,

Numerous industrial fields, like supply chain management, face mixed-integer optimization problems on a regular basis. Such problems typically show a sparse structure and vary in size, as well as complexity. However, in order to satisfy customer demands, it is crucial to find good solutions to all such problems quickly. Current research often focuses on the … Read more

The Vehicle Routing Problem with Access Restrictions

Categories Applications - OR and Management Sciences, Production and Logistics, Transportation Tags , , , ,

To mitigate the negative effect of freight vehicles on urban areas, many cities have implemented road accessibility restrictions, including limited traffic zones, which restrict access to specific areas during certain times of the day. Implementing these zones creates a trade-off between the delivery cost and time, even under the assumption of equal traversal time and … Read more

Improved Rank-One-Based Relaxations and Bound Tightening Techniques for the Pooling Problem

Categories Applications - Science and Engineering Tags , , ,

The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in some intermediate tanks, and mixed again to obtain the final products with desired specifications. The analysis of the pooling … Read more

A Tailored Derivative Instrument to Mitigate the Price-and-Quantity Risk faced by Wind Power Companies

Categories Energy, Finance and Economics Tags , , , , ,

The intermittent nature of wind generation combined with the well-known volatility of electricity spot prices expose Wind Power Companies (WPCs) committed to long-term forward contracts to the so-called price-and-quantity risk. Several instruments were designed in the past years to mitigate this risk exposure. However, most of them were mainly constructed to cope with only one … Read more