@inproceedings{varga_nagy_2023, title={NUMERICAL COMPARISON OF LONG-STEP INTERIOR POINT ALGORITHMS FOR SOLVING LINEAR COMPLEMENTARITY PROBLEMS}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85179517437&partnerID=MN8TOARS}, booktitle={Proceedings of the 17th International Symposium on Operational Research in Slovenia, SOR 2023}, author={Varga, A. and Nagy, M.E.}, year={2023}, pages={411–414} }
 @article{sufficient matrices: properties, generating and testing_2024, volume={202}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85168324290&partnerID=MN8TOARS}, DOI={10.1007/s10957-023-02280-7}, abstractNote={Abstract This paper investigates various aspects of sufficient matrices, one of the most relevant matrix classes introduced in connection with linear complementarity problems. We summarize the most important theoretical results and properties related to sufficient matrices. Based on these, we propose different construction rules that can be used to generate new matrices that belong to this class. A nonnegative number can be assigned to each sufficient matrix, which is called its handicap and works as a measure of sufficiency. The handicap plays a crucial role in proving convergence and complexity results for interior point algorithms for linear complementarity problems. For a particular sufficient matrix, called Csizmadia’s matrix, we give the exact value of the handicap, which is exponential in the size of the matrix. Another important topic that we address is deciding whether a matrix is sufficient. Tseng proved in 2000 that this decision problem is co-NP hard. We investigate three different algorithms for determining the sufficiency of a given matrix: Väliaho’s algorithm, a linear programming-based algorithm, and an algorithm that facilitates nonlinear programming reformulations of the definition of sufficiency. We tested the efficiency of these methods on our recently launched benchmark data set that consists of four different sets of matrices. In this paper, we give the description and most important properties of the benchmark set, which can be used in the future to compare the performance of different interior point algorithms for linear complementarity problems.}, number={1}, journal={Journal of Optimization Theory and Applications}, year={2024}, pages={204–236} }
 @article{marianna_varga_2022, title={A New Ai–Zhang Type Interior Point Algorithm for Sufficient Linear Complementarity Problems}, volume={202}, url={http://dx.doi.org/10.1007/s10957-022-02121-z}, DOI={10.1007/s10957-022-02121-z}, abstractNote={Abstract In this paper, we propose a new long-step interior point method for solving sufficient linear complementarity problems. The new algorithm combines two important approaches from the literature: the main ideas of the long-step interior point algorithm introduced by Ai and Zhang and the algebraic equivalent transformation technique proposed by Darvay. Similar to the method of Ai and Zhang, our algorithm also works in a wide neighborhood of the central path and has the best known iteration complexity of short-step variants. However, due to the properties of the applied transforming function in Darvay’s technique, the wide neighborhood definition in the analysis depends on the value of the handicap. We implemented not only the theoretical algorithm but a greedy variant of the new method (working in a neighborhood independent of the handicap) in MATLAB and tested its efficiency on both sufficient and non-sufficient problem instances. In addition to presenting our numerical results, we also make some interesting observations regarding the analysis of Ai–Zhang type methods.}, number={1}, journal={Journal of Optimization Theory and Applications}, author={Marianna, E.-Nagy and Varga, Anita}, year={2022}, month={Oct}, pages={76–107} }
 @article{marianna_varga_2023, title={A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation}, volume={31}, url={https://doi.org/10.1007/s10100-022-00812-6}, DOI={10.1007/s10100-022-00812-6}, abstractNote={Abstract In this paper, we investigate a new primal-dual long-step interior point algorithm for linear optimization. Based on the step size, interior point algorithms can be divided into two main groups, short-step, and long-step methods. In practice, long-step variants perform better, but usually, a better theoretical complexity can be achieved for the short-step methods. One of the exceptions is the large-update algorithm of Ai and Zhang. The new wide neighborhood and the main characteristics of the presented algorithm are based on their approach. In addition, we use the algebraic equivalent transformation technique of Darvay to determine new modified search directions for our method. We show that the new long-step algorithm is convergent and has the best known iteration complexity of short-step variants. We present our numerical results and compare the performance of our algorithm with two previously introduced Ai-Zhang type interior point algorithms on a set of linear programming test problems from the Netlib library.}, number={3}, journal={Central European Journal of Operations Research}, author={Marianna, E.-Nagy and Varga, Anita}, year={2023}, month={Sep}, pages={691–711} }
 @phdthesis{varga_2022, title={New Ai-Zhang type long-step interior point algorithms using the algebraically equivalent transformation technique}, school={Budapest University of Technology and Economics (Hungary)}, author={Varga, Anita}, year={2022} }
 @inproceedings{nagy_varga_2021, title={A NUMERICAL COMPARISON OF LONG-STEP INTERIOR POINT ALGORITHMS FOR LINEAR OPTIMIZATION}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85125174431&partnerID=MN8TOARS}, booktitle={Proceedings of the 16th International Symposium on Operational Research in Slovenia, SOR 2021}, author={Nagy, M.E. and Varga, A.}, year={2021}, pages={75–80} }
 @article{mályusz_varga_2018, title={An estimation of the learning curve effect on project duration with Monte Carlo simulation}, volume={49}, number={1}, journal={Periodica Polytechnica Architecture}, author={Mályusz, Levente and Varga, Anita}, year={2018}, pages={66–71} }
 @article{molnár-szipai_varga_2019, title={Integrating combinatorial algorithms into a linear programming solver}, volume={27}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85047306518&partnerID=MN8TOARS}, DOI={10.1007/s10100-018-0552-9}, number={2}, journal={Central European Journal of Operations Research}, author={Molnár-Szipai, R. and Varga, A.}, year={2019}, pages={475–482} }
 @inproceedings{mályusz_varga_2017, title={An Estimation of the Learning Curve Effect on Project Scheduling with Calendar Days Calculation}, volume={196}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85030467715&partnerID=MN8TOARS}, DOI={10.1016/j.proeng.2017.08.001}, abstractNote={Although learning is an essential part of life, traditional scheduling techniques cannot efficiently handle this effect. Considering the effects of the learning curve, it is possible to make a better prediction of project duration thus saving time and money. In this paper, a learning curve (or experience curve) effect on project duration is shown and calculated with calendar days. In the literature, project scheduling has been studied; however, only a few papers take the learning effect on project duration into consideration. The learning effect on project duration with the help of test problems and real problems was investigated. In test problems learning curve effect can occur between two consecutive activities. These pairs are chosen randomly. After calculating project duration, these pairs are allocated to be closer to each other using the predecessor's total float time. It is assumed that the duration of impending repetitive activities is shorter due to the learning curve effect if the gap between consecutive activities is small enough. This iteration is carried out until it is not possible to shorten the successor's activity time in a pair. It is shown that this effect brings a 1-3% shorter project duration. This "Calendar Days" calculation led to an integer programming problem that was solved by Matlab Parallel Computing Toolbox. 2.}, booktitle={Procedia Engineering}, author={Mályusz, L. and Varga, A.}, year={2017}, pages={730–737} }
 @inproceedings{mályusz_varga_2017, title={An Estimation of the Learning Effect on Project Cost Scheduling}, volume={196}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85030461747&partnerID=MN8TOARS}, DOI={10.1016/j.proeng.2017.07.239}, abstractNote={The effect of the learning phenomenon (learning curve) on project cost and scheduling is discussed in this paper. Although learning is an essential part of life, traditional scheduling techniques cannot efficiently handle the learning curve effect. It is assumed that the durations of impending repetitive activities, performed by the same workers, are shorter due to the learning curve effect, therefore no additional acceleration cost is necessary and the deployment cost before the second activity can also be neglected if the gap between consecutive activities is small enough. Taking into consideration the effects of the learning curve (or experience curve), it is possible to reduce project duration and cost. According to this study 0.4%-1% reduction in project cost and a 9-40% reduction in acceleration cost on a given project duration is available. Although the effect is a "simple" calculation, it leads to an exponential time algorithm if the learning effect is applied to traditional project scheduling techniques like Critical Path Method (CPM), or Precedence Diagramming Method (PDM). In this paper, an integer programming model is developed, and an efficient algorithm is used to estimate the project cost curve. The results are validated through an artificial example project.}, booktitle={Procedia Engineering}, author={Mályusz, L. and Varga, A.}, year={2017}, pages={723–729} }
 @article{mályusz_varga_2016, title={An estimation of the learning curve effect on project scheduling with working days calculation}, volume={47}, number={2}, journal={Periodica Polytechnica Architecture}, author={Mályusz, Levente and Varga, Anita}, year={2016}, pages={104–109} }