Related papers: A straightforward local-search optimization algori…
For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…
Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k-exchange neighborhood. This is the set of solutions that can be…
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…
We call an objective function or algorithm symmetric with respect to an input if after swapping two parts of the input in any algorithm, the solution of the algorithm and the output remain the same. More formally, for a permutation $\pi$ of…
Existing symmetry discovery methods predominantly focus on global transformations across the entire system or space, but they fail to consider the symmetries in local neighborhoods. This may result in the reported symmetry group being a…
In practice, objective functions of real-time control systems can have multiple local minimums or can dramatically change over the function space, making them hard to optimize. To efficiently optimize such systems, in this paper, we develop…
A random search algorithm intended to solve discrete optimization problems is considered. We outline the main components of the algorithm, and then describe it in more detail. We show how the algorithm can be implemented on parallel…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
We consider the problem of consistently matching multiple sets of elements to each other, which is a common task in fields such as computer vision. To solve the underlying NP-hard objective, existing methods often relax or approximate it,…
Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…
We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector…
We consider the query complexity of finding a local minimum of a function defined on a graph. This abstract problem is fundamental to many optimization tasks, such as finding a local minimum of the loss function when training deep neural…
Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph…