Optimization与一类多项式的NP_R-完备性
Optimization and NP_R-Completeness of Certain Fewnomials
摘要：
我们给出了一个高精度的多项式时间逼近方案的上确界的任何诚实的n-变量（n+2）-nomial与一个常数项，允许实指数以及实系数。我们的复杂性界限计数字段操作和不等式检查，并在n和一定的条件数的对数多项式。对于多项式的特殊情况（即，整数指数），我们的条件数的对数在稀疏编码中是二次的。在稀疏编码中，即使n是固定的，以前最好的复杂度界限也是指数的。在此过程中，我们将A-判别式理论推广到实指数和某些指数和，并发现了新的自然的NP_R-完全问题。
英文摘要：
We give a high precision polynomial-time approximation scheme for the supremum of any honest n-variate (n+2)-nomial with a constant term, allowing real exponents as well as real coefficients. Our complexity bounds count field operations and inequality checks, and are polynomial in n and the logarithm of a certain condition number. For the special case of polynomials (i.e., integer exponents), the log of our condition number is quadratic in the sparse encoding. The best previous complexity bounds were exponential in the sparse encoding, even for n fixed. Along the way, we extend the theory of A-discriminants to real exponents and certain exponential sums, and find new and natural NP_R-complete problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
