Parabolic Target-Space Interior-Point Algorithm for Weighted Monotone Linear Complementarity Problem

Anstreicher, K.M.: Interior-point algorithms for a generalization of linear programming and weighted
centering. Optim. Methods Softw. 27(4-5), 605–612 (2012)

Bazaraa, M.S., Sherali, H.D., Shetty., C.M.: Nonlinear programming: Theory and algorithms. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, third edition (2006)

Cottle, R.W., Pang, J.-S., Venkateswaran, V.: Sufficient matrices and the linear complementarity problem.
Linear Algebra Appl. 114-115, 231-249 (1989)

Cottle, R.W., Pang, J.-S., Stone., R.E.: The Linear Complementarity Problem. Computer Science and
Scientific Computing. Academic Press, Inc., Boston (1992)

Csizmadia, Zs., Illés, T.: New criss-cross type algorithms for linear complementarity problems with sufficient
matrices. Optim. Methods Softw. 21(2), 247–266 (2006)

Csizmadia, Zs., Illés, T., Nagy, A.: The s-Monotone Index Selection Rule for Criss-Cross Algorithms of
Linear Complementarity Problems. Acta Univ. Sapientiae Inform. 5(1), 103-139 (2013)

Darvay, Zs., Illés, T., Povh, J., Rigó, P.R.: Feasible Corrector-Predictor Interior-Point Algorithm for P∗(κ)-
Linear Complementarity Problems Based on a New Search Direction. SIAM J. Optim. 30(3), 2628-2658
(2020)

Darvay, Zs., Illés, T. Rigó, P.R.: Predictor-corrector interior-point algorithm for P∗(κ)-linear complementarity
problems based on a new type of algebraic equivalent transformation technique. Eur. J. Oper. Res. 299(1),
25–35 (2022)

de Klerk, E., Roos, C., Terlaky, T.: Nonlinear optimization [Hungarian translation]. In the series on
Operations Research, Aula Kiadó, Budapest (2004)

Fiacco, A.V., McCormick., G.P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques,
Wiley, New York (1968)

Glineur, F.: Topics in Convex Optimization: Interior-Point Methods, Conic Duality and Approximations. PhD Thesis, Faculté Polytechnique de Mons, Mons, Belgium (2001)

Gonzaga, C.C.: An Algorithm for Solving Linear Programming Problems in O(n3L) Operations. In: Megiddo, N. (eds.) Progress in Mathematical Programming. Springer, New York, NY (1989)

Illés, T., Roos, C., Terlaky, T.: Simple approach for the interior point theory of linear complementarity
problems with P∗ matrices. Unpublished manuscript (1997)

Illés, T., Peng, J., Roos, C., Terlaky, T.: A Strongly Polynomial Rounding Procedure Yielding a Maximally
Complementary Solution for P∗(κ) Linear Complementarity Problems. SIAM J. Optim. 11(2), 320-340
(2000)

Illés, T., Nagy, M., Terlaky, T.: A polynomial path-following interior point algorithm for general linear
complementarity problems. J. Global Optim. 47(3), 329-342 (2010)

Illés, T., Rigó, P.R., Török, R.: Unified Approach of Interior-Point Algorithms for P∗(κ)-LCPs Using a New
Class of Algebraically Equivalent Transformations. J. Optim. Theory Appl. 202(1), 27-49 (2024)

Klafszky, E., Terlaky, T.: Some generalizations of the criss-cross method for quadratic programming.
Optimization. 24(1-2), 127-139 (1992)

Kojima, M., Megiddo, N., Noma, T., Yoshise, A.: A Unified Approach to Interior Point Algorithms for Linear
Complementarity Problems. Lecture Notes in Comput. Sci. 538, Springer Verlag, Berlin, Germany (1991)

Martos, B.: Nonlinear Programming: Theory and Methods. Akadémiai Kiadó, Budapest (1975)

Megiddo, N.: Pathways to the optimal set in linear programming. In: N. Megiddo (ed.) Progress in Mathematical
Programming: Interior Point and Related Methods, pp. 131-158. Springer Verlag, New York (1989)

Nagy, M.: Interior point algorithms for general linear complementarity problems. PhD Thesis, Eötvös Loránd
University of Sciences, Institute of Mathematics, Budapest, Hungary (2009)

Nemirovski, A.: Interior point polynomial time methods in convex programming. Lecture Notes, Spring Semester, Georgia Institute of Technology, Atlanta, GA (1996)

Nesterov, Yu., Nemirovski, A.: Interior point polynomial methods in convex programming: Theory and
Applications, SIAM, Philadelphia (1994)

Nesterov, Yu.: Introductury Lectures on Convex Optimization. Kluwer Academic Publishers, Dordrecht
(2004)

Nesterov, Yu: Parabolic target space and primal–dual interior-point methods. Discrete Appl. Math. 156, 2079-
2100 (2008)

Nesterov, Yu.: Lectures on Convex Optimization. Springer Optimization and Its Applications, Springer,
Switzerland (2018)

Potra, F.A.: Weighted Complementarity Problems-A New Paradigm for Computing Equilibria. SIAM J. Optim. 22(4), 1634-1654 (2012)

Potra, F.A.: Sufficient weighted complementarity problems. Comput. Optim. Appl. 64, 467–488 (2016)

Renegar, J.: A polynomial-time algorithm, based on Newton’s method, for linear programming. Math. Program. 40, 59–93 (1988)

Renegar, J.: A mathematical view of interior-point methods in convex optimization. MPS/SIAM Ser. Optim, vol. 3, SIAM, New York (2001)

Török, R.: Test examples about linear complementarity problems. https://sites.google.com/view/lcp-testexamples-
roland-trk/mainpage (2023)

Sonnevend, Gy.: An ”analytic center” for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming. In: A. Prékopa, J. Szelezs´an, B. Strazicky (eds.) System Modelling and Optimization: Proceedings of the 12th IFIP-Conference, Budapest, Hungary, Lecture Notes in Control and Information Sciences 84, pp. 866-876. Springer Verlag, Berlin (1986)

Väliaho, H.: P∗-matrices are just sufficient. Linear Algebra Appl. 239, 103-108 (1996)

Ye, Y.: A path to the Arrow-Debreu competitive market equilibrium. Math. Program. 111, 315–348 (2008)