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- Hayato Waki, Sunyoung Kim, Masakazu Kojima, Masakazu Muramatsu
- SIAM Journal on Optimization
- 2006

Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in theâ€¦ (More)

Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in theâ€¦ (More)

- Hayato Waki, Sunyoung Kim, Masakazu Kojima, Masakazu Muramatsu, Hiroshi Sugimoto
- ACM Trans. Math. Softw.
- 2008

SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed byâ€¦ (More)

We propose a new relaxation scheme for the MAX-CUT problem using second-order cone programming. We construct relaxation problems to reflect the structure of the original graph. Numerical experimentsâ€¦ (More)

- Takashi Tsuchiya, Masakazu Muramatsu
- SIAM Journal on Optimization
- 1995

In this paper we present new global convergence results on a long-step affine scaling algorithm obtained by means of the local Karmarkar potential functions. This development was triggered by Dikinâ€™sâ€¦ (More)

- Hayato Waki, Masakazu Muramatsu
- J. Optimization Theory and Applications
- 2013

To obtain a primal-dual pair of conic programming problems having zero duality gap, two methods have been proposed: the facial reduction algorithm due to Borwein and Wolkowicz [1, 2] and the conicâ€¦ (More)

- Masakazu Kojima, Masakazu Muramatsu
- Comp. Opt. and Appl.
- 2009

This short note extends the sparse SOS (sum of squares) and SDP (semidefinite programming) relaxation proposed by Waki, Kim, Kojima and Muramatsu for normal POPs (polynomial optimization problems) toâ€¦ (More)

- Kunihito Hoki, Masakazu Muramatsu
- Entertainment Computing
- 2012

The efficiency of three forward-pruning techniques, i.e., futility pruning, null-move pruning, and LMR, is analyzed in shogi, a Japanese chess variant. It is shown that the techniques with the aâ€“bâ€¦ (More)

- Masakazu Muramatsu, Takashi Nagatani
- Physical review. E, Statistical physics, plasmasâ€¦
- 1999

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave isâ€¦ (More)

The Commutative Class of search directions for semidefinite programming is first proposed by Monteiro and Zhang [13]. In this paper, we investigate the corresponding class of search directions forâ€¦ (More)