Related papers: Convex Relaxation for Optimal Fixture Layout Desig…
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)…
Exact solution of hard combinatorial optimization problems often relies on strong convex relaxations, but solving these relaxations repeatedly inside a branch-and-bound algorithm can be prohibitively expensive. Hence, we consider this…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
The semidefinite programming (SDP) relaxation has proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem (QAP), arguably one of the hardest NP-hard…
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,…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
This paper presents a convex optimization framework for eco-driving and vehicle energy management problems. We will first show that several types of eco-driving and vehicle energy management problems can be modelled using the same notions…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
Convex relaxations of nonconvex multilabel problems have been demonstrated to produce superior (provably optimal or near-optimal) solutions to a variety of classical computer vision problems. Yet, they are of limited practical use as they…
In modern data analysis, one is frequently faced with statistical inference problems involving massive datasets. Processing such large datasets is usually viewed as a substantial computational challenge. However, if data are a…
We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel-accurate solution to multilabel problems. We show that previously proposed functional lifting…