Related papers: On The Optimization of Dijkstras Algorithm
In real-world optimization scenarios, the problem instance that we are asked to solve may change during the optimization process, e.g., when new information becomes available or when the environmental conditions change. In such situations,…
The multi-gradient descent algorithm (MGDA) finds a common descent direction that can improve all objectives by identifying the minimum-norm point in the convex hull of the objective gradients. This method has become a foundational tool in…
We describe two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line in that they react to updates on the data, keeping the simplification up-to-date. The supported updates…
We propose a generalization of the Weierstrass iteration for over-constrained systems of equations and we prove that the proposed method is the Gauss-Newton iteration to find the nearest system which has at least $k$ common roots and which…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of…
The "fast iterative shrinkage-thresholding algorithm", a.k.a. FISTA, is one of the most well-known first-order optimisation scheme in the literature, as it achieves the worst-case $O(1/k^2)$ optimal convergence rate in terms of objective…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This paper presents and experiments approaches to solve a new bi-objective routing problem called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a graph while optimizing two kinds of cost. The…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
Group testing is a well-known search problem that consists in detecting of $s$ defective members of a set of $t$ samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all…
This paper proposes two novel distributed continuous-time algorithms inspired by PID control to solve distributed optimization problems. The algorithms are referred to as first-order and second-order, respectively, depend on the intrinsic…
This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems.It shows that such information can significantly enhance performance, but that the choice of…
This paper deals with the problem of finding, for a given graph and a given natural number k, a subgraph of k nodes with a maximum number of edges. This problem is known as the k-cluster problem and it is NP-hard on general graphs as well…
In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the pro-posed strategy shares an (almost) identical network structure and…
We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with…
Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as…
In this work we advance the understanding of the fundamental limits of computation for Binary Polynomial Optimization (BPO), which is the problem of maximizing a given polynomial function over all binary points. In our main result we…
Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address…