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In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
Compressing resource-intensive large language models by removing whole transformer blocks is a seemingly simple idea, but identifying which blocks to remove constitutes an exponentially difficult combinatorial problem. In this paper, we…
The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as…
Traffic flows in a distributed computing network require both transmission and processing, and can be interdicted by removing either communication or computation resources. We study the robustness of a distributed computing network under…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
Two very important problems regarding spreading phenomena in complex topologies are the optimal selection of node sets either to minimize or maximize the extent of outbreaks. Both problems are nontrivial when a small fraction of the nodes…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to…
(Block-)coordinate minimization is an iterative optimization method which in every iteration finds a global minimum of the objective over a variable or a subset of variables, while keeping the remaining variables constant. While for some…
The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…