Related papers: Aggregation of Bilinear Bipartite Equality Constra…
Recently, we proposed a class of inequalities called lifted bilinear cover inequalities, which are second-order cone representable convex inequalities, and are valid for a set described by a separable bilinear constraint together with…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…
This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving…
Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…
Finding the exact integrality gap $\alpha$ for the LP relaxation of the 2-edge-connected spanning multigraph problem (2EC) is closely related to the same problem for the Held-Karp relaxation of the metric traveling salesman problem (TSP).…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they…
Power system optimization models are large mathematical models used by researchers and policymakers that pose tractability issues when representing real-world systems. Several aggregation techniques have been proposed to address these…
In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when…
Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide finite-time guarantees for converging algorithms, suited…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae which coalesce due to molecular diffusion. Owing…