Global ETD Search
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Showing 1 to 7 of 7 for “"multivariate polynomial"”.
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Set-based Particle Swarm Optimisation for Dynamic Optimisation Problems
… combinatorial optimisation problems and dynamic multivariate regression problems, which involve bilevel optimisation over both continuous and discrete domains. After a review of relevant optimisation theory and related literature, the thesis first investigates strategies that improve the …
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Grobner Bases and Ideals of Points
… Buchberger's Algorithm, in which the notion of S-polynomials is introduced, and a few modified or improved versions of Grobner basis algorithm are reviewed in this paper. In Chapter 1, we have a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division …
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Approximate Dynamic Programming with Applications
… towards the optimal value function. A multivariate polynomial relaxation algorithm is proposed for linearly constrained discrete time optimal control problems with convex cost. Relaxed value iteration is studied for constrained linear systems with convex piecewise linear cost. It is …
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New Techniques for Polynomial System Solving
Since any encryption map may be viewed as a polynomial map between finite dimensional vector spaces over finite fields, the security of a cryptosystem can be examined by studying the difficulty of solving large systems of multivariate polynomial equations. Therefore, algebraic attacks lead to the …
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Verificación formal en ACL2 del algoritmo de Buchberger
… Grobner bases computation in ACL2 in which: (1) Multivariate polynomial rings are formalized. This formalization is abstract: it encapsulates a coefficient ring which is used for the construction of polynomials and the verification of their properties. (2) These rings are equipped with an …
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Algebraic relaxations and hardness results in polynomial optimization and Lyapunov analysis
… and algebraic aspects of convexity in polynomial optimization. We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a …
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Security of Unbalanced Oil-Vinegar Signature Scheme
… ideas for oil-vinegar signature schemes in the multivariate polynomialcryptography.</p><p>In the first half, we focus on TTS (Tame Transformation Signature) systems. We find a structure attack to defeat a family of TTS systems. Then we have the related complexity analysis to claim that a family …