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- Heinz H. Bauschke, José Yunier Bello Cruz, Tran T. A. Nghia, Hung M. Phan, Xianfu Wang
- Journal of Approximation Theory
- 2014

The Douglas–Rachford splitting algorithm is a classical optimization method that has found many applications. When specialized to two normal cone operators, it yields an algorithm for finding a point in the intersection of two convex sets. This method for solving feasibility problems has attracted a lot of attention due to its good performance even in… (More)

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced… (More)

- Heinz H. Bauschke, D. Russell Luke, Hung M. Phan, Xianfu Wang
- Foundations of Computational Mathematics
- 2014

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. In this paper we consider the elementary method of alternating projections (MAP) for solving the sparsity… (More)

- Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan
- J. Optimization Theory and Applications
- 2012

This paper pursues a twofold goal. First to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction apply to deriving necessary optimality conditions for the optimistic version of bilevel programs… (More)

- Hung M. Phan, Boris S. Mordukhovich, HUNG M. PHAN, WAYNE STATE
- 2014

In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometric theory of variational analysis. We present their applications to calculus and optimality conditions for… (More)

- Heinz H. Bauschke, Ngoc Minh Dao, Dominikus Noll, Hung M. Phan
- J. Global Optimization
- 2016

- Huynh Cao, Hung Phan, Li-Xi Yang
- Anticancer research
- 2012

Hepatocellular carcinoma (HCC) is the fifth most common cancer and it is the third leading cause of cancer-related deaths worldwide. Once diagnosed with the disease, only 30-40% of patients are deemed eligible for curative intention with treatment modalities including surgical resection, liver transplantation, and chemoembolization. Eventually, most… (More)

- Boris S. Mordukhovich, Hung M. Phan
- Math. Program.
- 2012

This paper contains selected applications of the new tangential extremal principles and related results developed in [20] to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.

- Heinz H. Bauschke, José Yunier Bello Cruz, Tran T. A. Nghia, Hung M. Phan, Xianfu Wang
- Numerical Algorithms
- 2015

We systematically study the optimal linear convergence rates for several relaxed alternating projection methods and the generalized Douglas-Rachford splitting methods for finding the projection on the intersection of two subspaces. Our analysis is based on a study on the linear convergence rates of the powers of matrices. We show that the optimal linear… (More)

- Boris S. Mordukhovich, Hung M. Phan
- Math. Program.
- 2012

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite… (More)