Approximation Algorithms for Discrete Polynomial Optimization
نویسندگان
چکیده
منابع مشابه
Approximation Algorithms for Discrete Polynomial Optimization
In this paper, we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete (typically binary) variables. Such models have natural applications in graph theory, neural networks, error-correcting codes, among many others. In particular, we focus on three types of optimization models: (1) maximizing a homogeneous polynomial function in binary variable...
متن کاملApproximation algorithms for homogeneous polynomial optimization with quadratic constraints
In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions are nonconvex in general, t...
متن کاملDeterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems
Due to their fundamental nature and numerous applications, sphere constrained polynomial optimization problems have received a lot of attention lately. In this paper, we consider three such problems: (i) maximizing a homogeneous polynomial over the sphere; (ii) maximizing a multilinear form over a Cartesian product of spheres; and (iii) maximizing a multiquadratic form over a Cartesian product ...
متن کاملPolynomial-Time Approximation Algorithms
• Assume that the input is random, and find an algorithm that will perform well in the average case. For example, the maximum clique problem, which is NP -hard, can actually be solved efficiently assuming a random input because the maximum clique in a randomly chosen graph is small. This assumption is often used in practice, but the problem is that not everyone will agree on whether the input d...
متن کاملCsc5160: Combinatorial Optimization and Approximation Algorithms Topic: Polynomial Time Approximation Scheme 17.1 Polynomial Time Approximation Scheme 17.2 Knapsack Problem
In previous chapters we have seen the definition of a constant factor approximation algorithm. In this chapter, we will introduce the notion of a polynomial time approximation scheme (PTAS), which allows approximability to any required degree. To illustrate how PTAS works, we will study two examples, including the knapsack problem and the bin packing problem. The dynamic programming technique w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Operations Research Society of China
سال: 2013
ISSN: 2194-668X,2194-6698
DOI: 10.1007/s40305-013-0003-1