References of "Borwein, J. M"
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See detailRecent Results on Douglas–Rachford Methods for Combinatorial Optimization Problems
Aragón Artacho, Francisco Javier UL; Borwein, J. M.; Tam, M. K.

in Journal of Optimization Theory & Applications (in press)

We discuss recent positive experiences applying convex feasibility algorithms of Douglas-Rachford type to highly combinatorial and far from convex problems.

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See detailApplications of convex analysis within mathematics
Aragón Artacho, Francisco Javier UL; Borwein, J. M.; Martín-Márquez, V. et al

in Mathematical Programming (in press)

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of ... [more ▼]

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis. [less ▲]

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See detailDouglas-Rachford Feasibility Methods for Matrix Completion Problems
Aragón Artacho, Francisco Javier UL; Borwein, J. M.; Tam, M. K.

in ANZIAM Journal (2014), 55(4), 299-326

In this paper we give general recommendations for successful application of the Douglas-Rachford reflection method to convex and non-convex real matrix-completion problems. These guidelines are ... [more ▼]

In this paper we give general recommendations for successful application of the Douglas-Rachford reflection method to convex and non-convex real matrix-completion problems. These guidelines are demonstrated by various illustrative examples. [less ▲]

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See detailWalking on Real Numbers
Aragón Artacho, Francisco Javier UL; Bailey, D. H.; Borwein, J. M. et al

in Mathematical Intelligencer (2013), 35(1), 42-60

Motivated by the desire to visualize large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar(or three dimensional) walks and for ... [more ▼]

Motivated by the desire to visualize large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar(or three dimensional) walks and for quantitatively measuring their “randomness.” [less ▲]

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See detailRecent Results on Douglas–Rachford Methods
Aragón Artacho, Francisco Javier UL; Borwein, J. M.; Tam, M. K.

in Serdica Mathematical Journal (2013), 39

Recent positive experiences applying convex feasibility algorithms of Douglas–Rachford type to highly combinatorial and far from convex problems are described.

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See detailGlobal convergence of a non-convex Douglas-Rachford iteration
Aragón Artacho, Francisco Javier UL; Borwein, J. M.

in Journal of Global Optimization (2013), 57(3), 753-769

We establish a region of convergence for the proto-typical non-convex Douglas–Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration ... [more ▼]

We establish a region of convergence for the proto-typical non-convex Douglas–Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration Borwein and Sims (Fixed-point algorithms for inverse problems in science and engineering, pp. 93–109, 2011) was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given. [less ▲]

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