Related papers: Solution-space structure of (some) optimization pr…
In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
We study linear bilevel programming problems whose lower-level objective is given by a random cost vector with known distribution. We consider the case where this distribution is nonatomic, allowing to reformulate the problem of the leader…
Resource allocation problems in many computer systems can be formulated as mathematical optimization problems. However, finding exact solutions to these problems using off-the-shelf solvers in an online setting is often intractable for…
We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for…
This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
The minimum sum-of-squares clustering problem (MSSC) consists of partitioning $n$ observations into $k$ clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. In this paper, we propose…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
We study the problem of partitioning a set of $n$ objects in a metric space into $k$ clusters $V_1,\dots,V_k$. The quality of the clustering is measured by considering the vector of cluster costs and then minimizing some monotone symmetric…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We consider clustering problems where the goal is to determine an optimal partition of a given point set in Euclidean space in terms of a collection of affine subspaces. While there is vast literature on heuristics for this kind of problem,…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then…