Results 11 to 20 of about 1,360 (37)
The Lax conjecture is true [PDF]
, 2003 In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov.Comment: 7 pages, Proceedings to the ...
A. S. Lewis +3 more
core +5 more sources
On the linear convergence of the stochastic gradient method with constant step-size [PDF]
, 2018 The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size $\gamma$ (SGM-CS).
Cevher, Volkan, Vu, Bang Cong
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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
wiley +1 more source
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
wiley +1 more source
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
doaj +1 more source
On representations of the feasible set in convex optimization [PDF]
, 2009 We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex.
A. Ben-Tal +8 more
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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
wiley +1 more source
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
wiley +1 more source