Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in optimization. One difficulty is that the analysis can depend on the probability distribution of the inputs to the model. However, we show … Read more
In time dependent models, the objective is to find the optimal times (continuous) at which activities occur and resources are utilized. These models arise whenever a schedule of activities needs to be constructed. A common approach consists of discretizing the planning time and then restricting the decisions to those time points. However, this approach leads … Read more
In this paper, we aim at unifying, simplifying, and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce the notion of nice primal algorithmic map, which plays a central role in the unification and in the simplification of the analysis of all Lagrangian-based methods. Equipped with a nice primal … Read more
A weakly infeasible semidefinite program (SDP) has no feasible solution, but it has nearly feasible solutions that approximate the constraint set to arbitrary precision. These SDPs are ill-posed and numerically often unsolvable. They are also closely related to “bad” linear projections that map the cone of positive semidefinite matrices to a nonclosed set. We describe … Read more
Published in Annals of Operations Research. https://doi.org/10.1007/978-3-031-47859-8_26 Motivated by a routing problem faced by banks to enhance their encashment services in the city of Perm, Russia, we solve versions of the traveling salesman problem with clustering. To minimize the risk of theft, suppliers seek to operate multiple vehicles and determine an efficient routing; and, a single vehicle serves … Read more
In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer with suitable proximal parameter to each of the first grouped subproblems, we develop a partial LQP-based Alternating Direction Method of Multipliers (ADMM-LQP). The dual variable is updated twice with relatively larger … Read more
A new gradient stepsize is derived at the motivation of equipping the Barzilai-Borwein (BB) method with two dimensional quadratic termination property. A remarkable feature of the new stepsize is that its computation only depends on the BB stepsizes in previous iterations without the use of exact line searches and Hessian, and hence it can easily … Read more
In this paper, we introduce TITAN, a novel inerTial block majorIzation minimization framework for non-smooth non-convex opTimizAtioN problems. TITAN is a block coordinate method (BCM) that embeds inertial force to each majorization-minimization step of the block updates. The inertial force is obtained via an extrapolation operator that subsumes heavy-ball and Nesterov-type accelerations for block proximal … Read more
We consider a novel class of linear bilevel optimization models with a lower level that is a linear program with complementarity constraints (LPCC). We present different single-level reformulations depending on whether the linear complementarity problem (LCP) as part of the lower-level constraint set depends on the upper-level decisions or not as well as on whether … Read more
In this paper we consider the Combined Cell Layout Problem (CCLP), the Multi-Bay Facility Layout Problem (MBFLP) and several generalizations of the MBFLP, which have wide applications, e.g., in factory planning, heavy manufacturing, semiconductor fabrication and arranging rooms in hospitals. Given a set of cells of type single-row or directed-circular and a set of one-dimensional … Read more