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A gradient projection method for solving split equality and split feasibility problems in Hilbert spaces Phan, Vuong ; ; in Optimization A Journal of Mathematical Programming and Operations Research (2015) Detailed reference viewed: 65 (2 UL)Accelerating the DC algorithm for smooth functions Aragón Artacho, Francisco Javier ; Fleming, Ronan MT ; Phan, Vuong E-print/Working paper (2015) We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be ... [more ▼] We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be used to define a descent direction for the objective function evaluated at this point. Our algorithms are based on a combination of DCA together with a line search step that uses this descent direction. Convergence of the algorithms is proved and the rate of convergence is analysed under the Łojasiewicz property of the objective function. We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the Łojasiewicz property. Numerical tests on various biochemical models clearly show that our algorithms outperforms DCA, being on average more than four times faster in both computational time and the number of iterations. The algorithms are globally convergent to a non-equilibrium steady state of a biochemical network, with only chemically consistent restrictions on the network topology. [less ▲] Detailed reference viewed: 141 (16 UL)Extragradient methods and linesearch algorithms for solving Ky Fan inequalities and fixed point problems Phan, Vuong ; ; in Journal of Optimization Theory & Applications (2012) In this paper, we introduce some new iterative methods for finding a common element of the set of points satisfying a Ky Fan inequality, and the set of fixed points of a contraction mapping in a Hilbert ... [more ▼] In this paper, we introduce some new iterative methods for finding a common element of the set of points satisfying a Ky Fan inequality, and the set of fixed points of a contraction mapping in a Hilbert space. The strong convergence of the iterates generated by each method is obtained thanks to a hybrid projection method, under the assumptions that the fixed-point mapping is a ξ-strict pseudocontraction, and the function associated with the Ky Fan inequality is pseudomonotone and weakly continuous. A Lipschitz-type condition is assumed to hold on this function when the basic iteration comes from the extragradient method. This assumption is unnecessary when an Armijo backtracking linesearch is incorporated in the extragradient method. The particular case of variational inequality problems is examined in a last section. [less ▲] Detailed reference viewed: 96 (4 UL) |
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