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We propose a class of quadratic optimization problems whose exact optimal objective values can be computed by their completely positive cone programming relaxations. The objective function can be any quadratic form. The constraints of each problem are described in terms of quadratic forms with no linear terms, and all constraints are homogeneous equalities,(More)
For a quadratic optimization problem (QOP) with linear equality constraints in continuous nonnegative variables and binary variables, we propose three relaxations in simplified forms with a parameter λ: Lagrangian, completely positive, and copositive relaxations. These re-laxations are obtained by reducing the QOP to an equivalent QOP with a single(More)
We propose the moment cone relaxation for a class of polynomial optimization problems (POPs) to extend the results on the completely positive cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods(More)
In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified framework for conic and Lagrangian-conic relaxations of quadratic optimization problems (QOPs) and polynomial optimization problems (POPs). The framework is constructed with a linear conic optimization problem (COP) in a finite dimensional vector space endowed with an(More)
Functional studies of the interleukin 2 receptor (IL-2R) of two (ED515-D and Kit225) IL-2-dependent and three (ED515-I, 3T3-alpha beta 11, and Hut102) IL-2-independent cell lines were done. All of these cell lines appeared to express high as well as low affinity IL-2R. However, ED515-I and 3T3-alpha beta 11, which expressed the IL-2R beta chain, did not(More)
Leukemic cells in the peripheral blood of a patient with adult T cell leukemia (ATL), which expressed the Tac antigen/interleukin 2 (IL2) receptor, were investigated in vitro for autocrine growth by IL 2. The cells showed spontaneous proliferation in mitogen-free medium. The spontaneous proliferation of the cells was inhibited by monoclonal anti-IL 2 or(More)
We present the moment cone (MC) relaxation and a hierarchy of sparse Lagrangian-SDP relaxations of polynomial optimization problems (POPs) using the unified framework established in Part I. The MC relaxation is derived for a POP of minimizing a polynomial subject to a nonconvex cone constraint and polynomial equality constraints. It is an extension of the(More)
The Lagrangian-doubly nonnegative (DNN) relaxation has recently been shown to provide effective lower bounds for a large class of nonconvex quadratic optimization problems (QOPs) using the bisection method combined with first-order methods by Kim, Kojima and Toh in 2016. While the bisection method has demonstrated the computational efficiency, determining(More)