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Creators/Authors contains: "Tang, Xindong"

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  1. ; ; (, Science China Mathematics)
    Free, publicly-accessible full text available July 1, 2026
  2. ; ; ; (, Mathematical Programming)
    Abstract This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative polynomials, each of which belongs to the sum of the ideal and quadratic module generated by the corresponding sparse constraints. Based on this characterization, we give several sufficient conditions for the sparse Moment-SOS hierarchy to be tight. In particular, we show that this sparse hierarchy is tight under some assumptions such as convexity, optimality conditions or finiteness of constraining sets. 
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  3. ; ; (, SIAM Journal on Optimization)
    Full Text Available 
  4. ; (, Mathematics of Operations Research)
    This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Moment-sum-of-squares relaxations are used to solve them. Under generic assumptions, the method can find a Nash equilibrium, if there is one. Moreover, it can find all Nash equilibria if there are finitely many ones of them. The method can also detect nonexistence if there is no Nash equilibrium. Funding: J. Nie was supported by the National Science Foundation [Grant DMS-2110780]. 
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  5. ; ; ; (, Numerical Algebra, Control and Optimization)
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