In this paper, we study several classes of set-valued maps, which can be used in set-valued optimization and its applications, and their respective maximum and minimum value functions. The definitions of these maps are based on scalar-valued, vector-valued, and cone-valued maps. Moreover, we consider those extremal value functions which are obtained when optimizing linear functionals … Read more
We address three variants of the two-dimensional cutting stock problem in which the guillotine cutting of large objects produces a set of demanded items. The characteristics of the variants are: the rectangular shape of the objects and items; the number of two or three orthogonal guillotine stages; and, a sequencing constraint that limits the number … Read more
We consider a variant of the electric vehicle routing problem: a fleet of identical vehicles of limited capacity needs to visit a set of customers with given demands. An upper limit is imposed on the duration of the routes. Vehicles have limited autonomy: they may need to stop en-route at recharge stations. Recharges can be … Read more
This paper addresses the mathematical programs with cardinality constraints (MPCaC). We first define two new tailored (strong and weak) second-order necessary conditions, MPCaC-SSONC and MPCaC-WSONC. We then propose a constraint qualification (CQ), namely, MPCaC-relaxed constant rank constraint qualification (MPCaC-RCRCQ), and establish the validity of MPCaC-SSONC at minimizers under this new CQ. All the concepts proposed … Read more
This paper explores the logistics operations of instant grocery delivery services. We specifically concentrate on two widely adopted strategies: Personal Shopper Systems (PSS) and Inventory Owned Delivery Systems (IOD). In the PSS, couriers visit affiliated brick and mortar stores in the delivery area to pick and purchase ordered products and deliver them to customers. Whereas … Read more
Recently, there has been a paradigm shift by certain energy and chemical companies towards modular manufacturing, whereby transportable modular production units can be relocated between production facilities to meet the spatial and temporal changes in the availabilities, demands, and prices of the underlying commodities. We refer to the optimal distribution, production, and storage of commodities, … Read more
Most optimization problems arising in imaging science involve high-dimensional linear operators and their adjoints. In the implementations of these operators, approximations may be introduced for various practical considerations (e.g., memory limitation, computational cost, convergence speed), leading to an adjoint mismatch. This occurs for the X-ray tomographic inverse problems found in Computed Tomography (CT), where the … Read more
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method (RIPM), is for solving Riemannian constrained optimization problems. We establish its local superlinear and quadratic convergence under the standard assumptions. Moreover, we show its global convergence when it is combined with … Read more
The $p$-hub center problem is a fundamental model for the strategic design of hub location. It aims at constructing $p$ fully interconnected hubs and links from nodes to hubs so that the longest path between any two nodes is minimized. Existing literature on the $p$-hub center problem under uncertainty often assumes a joint distribution of … Read more
In this paper, we develop an Inexact Relaxed Augmented Lagrangian Method (IR-ALM) for solving a class of convex optimization problems. Flexible relative error criteria are designed for approximately solving the resulting subproblem, and a relaxation step is exploited to accelerate its convergence numerically. By a unified variational analysis, we establish the global convergence of this … Read more