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Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
Mixed-Integer Linear Programs (MIPs) are powerful and flexible tools for modeling a wide range of real-world combinatorial optimization problems. Predict-and-Search methods operate by using a predictive model to estimate promising variable…
Although state-of-the-art (SOTA) SAT solvers based on conflict-driven clause learning (CDCL) have achieved remarkable engineering success, their sequential nature limits the parallelism that may be extracted for acceleration on platforms…
This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of…
In this paper, a new efficient computational algorithm is presented for solving cyclic heptadiagonal linear systems based on using of heptadiagonal linear solver and Sherman-Morrison-Woodbury formula. The implementation of the algorithm…
Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…
The at-most-k constraint is ubiquitous in combinatorial problems, and numerous SAT encodings are available for the constraint. Prior experiments have shown the competitiveness of the sequential-counter encoding for k $>$ 1, and have…
In recent years, the generation of rigorously provable chaos in finite precision digital domain has made a lot of progress in theory and practice, this article is a part of it. It aims to improve and expand the theoretical and application…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of $10^{-5}$, a concatenated scheme using RS…
Hashing has proven a valuable tool for large-scale information retrieval. Despite much success, existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of…
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…
The one of the most interesting problem of discrete mathematics is the SAT (satisfiability) problem. Good way in SAT solver developing is to transform the SAT problem to the problem of continuous search of global minimums of the functional…
When solving real-world problems, practitioners often hesitate to implement solutions obtained from mathematical models, especially for important decisions. This hesitation stems from practitioners' lack of trust in optimization models and…
Networks found with Neural Architecture Search (NAS) achieve state-of-the-art performance in a variety of tasks, out-performing human-designed networks. However, most NAS methods heavily rely on human-defined assumptions that constrain the…
Recent research has examined algorithms to minimize robots' resource footprints. The class of combinatorial filters (discrete variants of widely-used probabilistic estimators) has been studied and methods for reducing their space…
The Boolean Satisfiability problem (SAT), as the prototypical $\mathsf{NP}$-complete problem, is crucial in both theoretical computer science and practical applications. To address this problem, stochastic local search (SLS) algorithms,…