Article
Automation & Control Systems
Agniva Chowdhury, Gregory Dexter, Palma London, Haim Avron, Petros Drineas
Summary: Linear programming is a useful tool that has been successfully applied in various fields. This paper focuses on the special case where the number of variables is much larger than the number of constraints and proposes a preconditioning technique to ensure the convergence and optimization of the algorithm.
JOURNAL OF MACHINE LEARNING RESEARCH
(2022)
Article
Operations Research & Management Science
Angelica Miluzca Victorio Celis, Jose Herskovits Norman
Summary: This paper proposes an improved algorithm for solving large-scale linear programming problems, reducing the solution time of linear systems to improve performance. Mathematical proofs and numerical evidence demonstrate the effectiveness of the method.
RAIRO-OPERATIONS RESEARCH
(2022)
Article
Mathematics, Applied
Stefania Bellavia, Jacek Gondzio, Margherita Porcelli
Summary: This paper introduces a new relaxed variant of interior point method for low-rank semidefinite programming problems, imposing a special nearly low-rank form of all primal iterates and approximating the first order optimality conditions by solving an auxiliary least-squares problem. The method allows for the computation of both primal and dual approximated Newton directions, and its convergence has been established, with promising preliminary computational results for solving SDP-reformulation of matrix-completion problems.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Software Engineering
Mathieu Tanneau, Miguel F. Anjos, Andrea Lodi
Summary: This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. Tulip is competitive with open-source interior-point solvers, and is flexible in handling unbounded and infeasible problems. It also demonstrates a tenfold speedup in structured master problems over state-of-the-art commercial interior point method solvers. Additionally, Tulip's ability to use different levels of arithmetic precision is illustrated through problems solved in extended precision.
MATHEMATICAL PROGRAMMING COMPUTATION
(2021)
Article
Computer Science, Interdisciplinary Applications
T. A. Espaas, V. S. Vassiliadis
Summary: This paper revisits the idea of employing higher-order derivatives of interior point trajectories within an algorithmic framework, emphasizing the importance of their expansion's radius of convergence. The significant computational results highlight the potential of using higher-order algorithms for certain problems, and the theoretical complexity analysis shows that a second-order trajectory-following algorithm for linear programming retains the iteration dependency of current primal-dual methods.
COMPUTERS & CHEMICAL ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Shaojun Zhu, Makoto Ohsaki, Kazuki Hayashi, Xiaonong Guo
Summary: This paper introduces the concept of machine-specified ground structures for topology optimization, which can generate sparse stable structures without the need for re-training for different-sized node-sets, effectively assisting structural topology design. In topology optimization problems, machine-specified ground structures have an advantage in achieving global optimal solutions.
ADVANCES IN ENGINEERING SOFTWARE
(2021)
Article
Mathematics, Applied
Lino M. Silva, Aurelio R. L. Oliveira
Summary: The interior-point method is efficient in solving large linear programming problems by reducing the time needed to solve linear systems, with techniques like incomplete Cholesky factorization as a preconditioner. Modifications to controlled Cholesky factorization can further decrease the need for refactorizations of diagonally modified matrices, ultimately improving the performance of the method.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Computer Science, Artificial Intelligence
Qi Zhao, Guangcan Liu, Qingshan Liu
Summary: The existing algorithms for sparse coding have two main defects: vector-based algorithms struggle with tensor signals, while tensor-based algorithms are not learnable yet. To address this dilemma, TLISTA model is proposed, which can effectively handle data in tensor form and achieve linear convergence rate.
Article
Chemistry, Multidisciplinary
Simon Silih, Zdravko Kravanja, Stojan Kravanja
Summary: This paper presents the Mixed-Integer Non-linear Programming (MINLP) approach for the synthesis of trusses, discussing the solution to continuous/discrete non-convex and non-linear optimization problems. It showcases the generation of different truss MINLP superstructures and the development of a special model formulation. The paper also introduces multi-level MINLP strategies to accelerate convergence and discusses the importance of local buckling constraints on topology optimization.
APPLIED SCIENCES-BASEL
(2022)
Article
Operations Research & Management Science
Fabio Vitor, Todd Easton
Summary: Most linear programming interior point algorithms update the interior solution by following a single search direction at each iteration. In contrast, two-dimensional search interior point algorithms use two search directions and solve a two-dimensional subspace linear program to find an improved interior solution. This paper introduces primal and dual two-dimensional search interior point algorithms based on affine and logarithmic barrier search directions.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2022)
Article
Operations Research & Management Science
Marianna E-Nagy, Anita Varga
Summary: This paper proposes a new long-step interior point method for solving sufficient linear complementarity problems, combining the ideas of the long-step interior point algorithm and the algebraic equivalent transformation technique. The algorithm works in a wide neighborhood of the central path and has the best known iteration complexity.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Operations Research & Management Science
Jianbin Wang, Jianhua Yuan, Wenbao Ai
Summary: This paper proposes a step-truncated technique in a path-following interior-point algorithm for linear programming, which achieves quadratic convergence without requiring a corrector step in the nondegenerate case. Numerical results demonstrate the advantages of the proposed method under the requirement of high precision.
OPTIMIZATION LETTERS
(2023)
Article
Mathematics, Applied
Valentina De Simone, Daniela di Serafino, Jacek Gondzio, Spyridon Pougkakiotis, Marco Viola
Summary: In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for large-scale optimization problems seeking sparse solutions. Computational experience on various problems demonstrates that interior point methods, equipped with suitable linear algebra, offer a noticeable advantage over first-order approaches.
Article
Computer Science, Interdisciplinary Applications
T. A. Espaas, V. S. Vassiliadis
Summary: This paper extends the concept of higher-order search directions in interior point methods to convex nonlinear programming. It provides the mathematical framework for computing higher-order derivatives and highlights simplified computation for special cases. The paper also introduces a dimensional lifting procedure for transforming general nonlinear problems into more efficient forms and describes the algorithmic development required to employ these higher-order search directions.
COMPUTERS & CHEMICAL ENGINEERING
(2024)
Article
Operations Research & Management Science
Zaoui Billel, Benterki Djamel, Kraria Aicha, Raouache Hadjer
Summary: We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. By applying a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system, we characterize the central path. Furthermore, we demonstrate that the algorithm finds the epsilon-optimal solution of the underlying problem in polynomial time. Finally, we conduct a comparative numerical study to analyze the efficiency of the proposed algorithm.
RAIRO-OPERATIONS RESEARCH
(2023)
Article
Computer Science, Interdisciplinary Applications
Tomasz Sokol, Tomasz Lewinski
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2016)
Editorial Material
Computer Science, Interdisciplinary Applications
Ming Zhou, Gregoire Allaire, Gengdong Cheng, Jianbin Du, Matthew Gilbert, Xu Guo, James Guest, Raphael Haftka, Alicia Kim, Thomas Lewinski, Kurt Maute, Julian Norato, Niels Olhoff, Glaucio H. Paulino, Tomasz Sokol, Michael Wang, Ren-Jye Yang, Byeng Dong Youn
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2016)
Article
Engineering, Multidisciplinary
T. Lewinski, S. Czarnecki, G. Dzierzanowski, T. Sokol
BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES
(2013)
Article
Computer Science, Interdisciplinary Applications
George I. N. Rozvany, Tomasz Sokol
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2012)
Editorial Material
Computer Science, Interdisciplinary Applications
Tomasz Sokol, George I. N. Rozvany
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2013)
Article
Computer Science, Interdisciplinary Applications
Tomasz Sokol, George I. N. Rozvany
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2012)
Editorial Material
Computer Science, Interdisciplinary Applications
Tomasz Sokol, George I. N. Rozvany
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2013)
Article
Computer Science, Interdisciplinary Applications
T. Lewinski, G. I. N. Rozvany, T. Sokol, K. Bolbotowski
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2013)
Article
Computer Science, Interdisciplinary Applications
George Rozvany, Vanda Pomezanski, Tomasz Sokol
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2014)
Article
Computer Science, Interdisciplinary Applications
George I. N. Rozvany, Tomasz Sokol, Vanda Pomezanski
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2014)
Article
Computer Science, Interdisciplinary Applications
Grzegorz Kozlowski, Tomasz Sokol
Summary: This paper presents an enhanced growth method for optimal design of plane trusses without the need for a ground structure, using virtual displacements and strains fields. The method has been applied to plastic design with stress and size constraints, and demonstrated reliability and accuracy through three examples.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Proceedings Paper
Engineering, Mechanical
T. Sokol
ADVANCES IN MECHANICS: THEORETICAL, COMPUTATIONAL AND INTERDISCIPLINARY ISSUES
(2016)
Proceedings Paper
Engineering, Mechanical
K. Bolbotowski, T. Sokol
ADVANCES IN MECHANICS: THEORETICAL, COMPUTATIONAL AND INTERDISCIPLINARY ISSUES
(2016)
Proceedings Paper
Computer Science, Theory & Methods
T. Sokol
RECENT ADVANCES IN COMPUTATIONAL MECHANICS
(2014)
