Results 11 to 20 of about 106 (96)
Journal of Applied Mathematics, Volume 2004, Issue 5, Page 409-431, 2004., 2004 We consider the problem of projecting a point onto a region defined by a linear equality or inequality constraint and two‐sided bounds on the variables. Such problems are interesting because they arise in various practical problems and as subproblems of gradient‐type methods for constrained optimization.
Stefan M. Stefanov
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Method for solving a convex integer programming problem
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 44, Page 2829-2834, 2003., 2003 We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.
Stefan M. Stefanov
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Iterative algorithms with seminorm‐induced oblique projections
Abstract and Applied Analysis, Volume 2003, Issue 7, Page 387-406, 2003., 2003 A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A block‐iterative algorithmic scheme for solving the
Yair Censor, Tommy Elfving
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A global method for some class of optimization and control problems
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 9, Page 605-616, 2000., 2000 The problem of maximizing a nonsmooth convex function over an arbitrary set is considered. Based on the optimality condition obtained by Strekalovsky in 1987 an algorithm for solving the problem is proposed. We show that the algorithm can be applied to the nonconvex optimal control problem as well.
R. Enkhbat
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EURO Journal on Computational Optimization, 2016 We analyze the proximal alternating linearized minimization algorithm (PALM) for solving non-smooth convex minimization problems where the objective function is a sum of a smooth convex function and block separable non-smooth extended real-valued convex ...
Ron Shefi, Marc Teboulle
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A proximal point method for nonsmooth convex optimization problems in Banach spaces
Abstract and Applied Analysis, Volume 2, Issue 1-2, Page 97-120, 1997., 1997 In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case.
Y. I. Alber, R. S. Burachik, A. N. Iusem
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General algorithm and sensitivity analysis for variational inequalities
International Journal of Stochastic Analysis, Volume 5, Issue 1, Page 29-41, 1992., 1991 The fixed point technique is used to prove the existence of a solution for a class of variational inequalities related to odd order boundary value problems, and to suggest a general algorithm. We also study the sensitivity analysis for these variational inequalities and complementarity problems using the projection technique.
Muhammad Aslam Noor
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Uncontrolled inexact information within bundle methods
EURO Journal on Computational Optimization, 2017 We consider convex non-smooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy ...
Jérôme Malick +2 more
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Two Relaxed Inertial Forward–Reflected–Backward Splitting Algorithms With Momentum Terms
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, to solve the monotone inclusion problem consisting of the sum of two monotone operators in Hilbert spaces, we propose and study two modifications of Malitsky–Tam’s forward–reflection–backward splitting methods with double momentum terms. Meanwhile, we consider a relaxed inertial version to expand the range of allowable step sizes.
Binbin Zhang +3 more
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Algebraic and metric structures of the geometric mean cone
Special MatricesThe geometric mean cone (GMC) is a higher-order generalization of the second-order cone and the rotated quadratic cone. While these lower-order cones admit well-established Euclidean Jordan algebraic representations, no analogous framework is currently ...
Alzalg Baha
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