M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 2 (2003) 125-144. Home/Search Document Details and Download
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An Extension of Sums of Squares Relaxations to . . . - Kojima, al. (2004) Self-citation (Kojima) (Correct)
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M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 2 (2003) 125-144.
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M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 (2003) 125-144.
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M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 2 (2003) 125-144.
Sums of Squares Relaxations of Polynomial Semidefinite Programs - Kojima (2003) Self-citation (Kojima) (Correct)
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M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 (2003) 125-144.
An Extension of Sums of Squares Relaxations to Polynomial.. - Kojima, al. (2004) Self-citation (Kojima) (Correct)
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M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 2 (2003) 125-144.
Generalized Lagrangian Duals and Sums of Squares Relaxations of.. - Kim, al. (2004) Self-citation (Kojima Kim Waki) (Correct)
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M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 2 (2003) 125-144.
Sparsity in Sums of Squares of Polynomials - Kojima, al. (2003) Self-citation (Kojima Kim Waki) (Correct)
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M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 2 (2003) 125-144.
Sparsity in Sums of Squares of Polynomials - Kojima, al. (2003) Self-citation (Kojima Kim Waki) (Correct)
....(of polynomials) global nonnegativity of the polynomial is guaranteed. Representing a polynomial as a sum of squares has gained a lot of attention in recent developments of sum of squares optimization [9, 10] and SDP (semidefinite programming) relaxation of polynomial optimization problems [5, 6, 7, 8]. When we aim to represent a nonnegative polynomial in terms of a sum of squares of polynomials, we need to address two issues of whether such representation is possible and how it can be computed. The first issue is studied by many researchers starting from Hilbert. See [14] The second ....
.... to have a polynomial with the coe#cients c # (w) # of f(x) as linear functions of a parameter vector w : f(x, w) c # (w)x , in many applications arising from sum of squares optimization problems [9, 10] and SDP (semidefinite programming) relaxation of polynomial optimization problems [5, 6, 7, 8]. It is an extension of (1) where the coe#cients c # (w) # of the polynomial f(x) are constant. The goal is to generate a small subset such that for each fixed w f(x, w) is sum of squares of a finite number of polynomials g (x, w) having a support G. Because the proposed ....
M. Kojima, S. Kim and H. Waki, "A general framework for convex relaxation of polynomial optimization problems over cones", Journal of Operations Research Society of Japan, 46 2 (2003) 125-144.
Second Order Cone Programming Relaxation of Positive.. - Kim, Kojima, Yamashtia (2001) Self-citation (Kojima Kim) (Correct)
....We have extended the SOCP relaxation in [5] by considering a more general form of the variable matrix of the SDP relaxation. This gives us flexibility to formulate SOCP relaxations, especially when deriving an effective SOCP relaxation is an important issue. In recent work by Kojima et al. [7], a new framework for convex relaxation of polynomial optimization problems over cones in terms of linear optimization problems (LOPs) over cones was presented. The framework provided various ways of formulating convex relaxation using LOPs over cones, of which SOCP relaxation was shown as a ....
M. Kojima, S. Kim and H. Waki (2002) "A general framework for convex relaxation of polynomial optimization problems over cones", Research Report B-380, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8552, Japan.
Lift-and-Project for 0-1 Programming via Algebraic Geometry - Zuluaga, Vera, Peña (2003) (Correct)
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M. Kojima, S. Kim and H. Waki, A General Framework for Convex Relaxation of Polynomial Optimization Problems over Cones, J. Oper. Res. Soc. Japan 46 (2003) 125-144.
Semidefinite and Cone Programming Bibliography/Comments - Wolkowicz (2004) (Correct)
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M. KOJIMA. A general framework for convex relaxation of polynomial optimization problems over cones. Technical Report B-380, Dept. of Mathematical Sciences, Tokyo Institute of Technology, Tokyo, Japan, 1998.
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