In the branch-and-bound algorithm, branching is the key step to deal with the nonconvexity of the problem. For Mixed Integer Linear Optimization (MILO) problems and, in general, Mixed Integer Nonlinear Optimization (MINLO) problems whose continuous relaxation is convex, branching on integer and binary variables suffices, because fixing all integer variables yields a convex relaxation. General, … Read more
This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a proximal bundle type method. Both functional and stationary complexity bounds for the two methods are established in terms of the unknown strong convexity parameter. To the best of our knowledge, the … Read more
Derivative-based iterative methods for nonlinearly constrained non-convex optimization usually share common algorithmic components, such as strategies for computing a descent direction and mechanisms that promote global convergence. Based on this observation, we introduce an abstract framework based on four common ingredients that describes most derivative-based iterative methods and unifies their workflows. We then present Uno, … Read more
This paper proposes and evaluates a Multi-Reference Relaxation Enforced Neighborhood Search (MRENS) heuristic within the SCIP solver. This study marks the first integration and evaluation of MRENS in a full-fledged MILP solver, specifically coupled with the recently-introduced Lagromory separator for generating multiple reference solutions. Computational experiments on the MIPLIB 2017 benchmark set show that MRENS, … Read more
In this work, we propose the joint use of a mixed penalty-logarithmic barrier approach and generating set search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, … Read more
We introduce a family of symmetric convex bodies called generalized ellipsoids of degree \(d\) (GE-\(d\)s), with ellipsoids corresponding to the case of \(d=0\). Generalized ellipsoids (GEs) retain many geometric, algebraic, and algorithmic properties of ellipsoids. We show that the conditions that the parameters of a GE must satisfy can be checked in strongly polynomial time, … Read more
Crowdshipping, a rapidly growing approach in Last-Mile Delivery (LMD), relies on independent crowdworkers for delivery orders. Building a sustainable network of crowdshippers is essential for the survival and growth of such systems, while their participation is primarily motivated by fair pay. Additionally, the financial well-being of crowdworkers is sensitive to fair compensation, especially for those … Read more
This paper provides a local convergence analysis for newly developed derivative-free methods in problems of smooth nonconvex optimization. We focus here on local convergence to local minimizers, which might be nonisolated and hence more challenging for convergence analysis. The main results provide efficient conditions for local convergence to arbitrary local minimizers under the fulfillment of … Read more
Given a simple graph G = (V, E) with vertex set V and edge set E, the minimum biclique cover problem seeks to cover all edges of the graph with a minimum number of bicliques (i.e., complete bipartite subgraphs). This paper proposes two compact mixed integer programming (MIP) formulations for solving the minimum biclique cover … Read more
We introduce a novel exact approach for addressing a broad spectrum of optimization problems with robust nonlinear constraints. These constraints are defined as sums of products of linear times concave (SLC) functions with respect to the uncertain parameters. Our approach synergizes a cutting set method with reformulation-perspectification techniques and branch and bound. We further extend … Read more