相关论文: Between steps: Intermediate relaxations between bi…

Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a…

In the preprocessing framework one is given a set of regions that one is allowed to preprocess to create some auxiliary structure such that when a realization of these regions is given, consisting of one point per region, this auxiliary…

In two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must…

When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…

We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…

In one of our earlier works, we proposed to approximate Pareto fronts to multiobjective optimization problems by two-sided approximations, one from inside and another from outside of the feasible objective set, called, respectively, lower…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

For a planar point set $P$, its convex hull is the smallest convex polygon that encloses all points in $P$. The construction of the convex hull from an array $I_P$ containing $P$ is a fundamental problem in computational geometry. By…

We show that the closed convex hull of any one-dimensional semi-algebraic subset of R^n has a semidefinite representation, meaning that it can be written as a linear projection of the solution set of some linear matrix inequality. This is…

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…

We study separation of a closed box from a max-min convex set by max-min semispace. This can be regarded as an interval extension of known separation results. We give a constructive proof of the separation in the case when the box and the…

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…

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…

For a certain class of distributions, we prove that the linear programming relaxation of $k$-medoids clustering---a variant of $k$-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn…

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 consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As…

For multi-limbed robots, motion planning with posture and force constraints tends to be a difficult optimization problem due to nonlinearities, which also present extended solve times. We propose a multi-stage optimization framework with…

Two commonly arising computational tasks in Bayesian learning are Optimization (Maximum A Posteriori estimation) and Sampling (from the posterior distribution). In the convex case these two problems are efficiently reducible to each other.…

We study sets defined as the intersection of a rank-1 constraint with different choices of linear side constraints. We identify different conditions on the linear side constraints, under which the convex hull of the rank-1 set is polyhedral…

We study the applicability of the Peaceman-Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function,…