Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions

Global optimal solutions to nonconvex optimisation problems with a sum of double-well and log-sum-exp functions

This paper presents a canonical dual approach for solving a nonconvex global optimisation problem with a sum of double-well and log-sum-exp functions. Such a problem arises extensively in mechanics, robot designing, information theory and network communication systems. It includes fourth-order polynomial minimisation problems and minimax problems. Based on the canonical duality theory, this non...

Global Optimization of Polynomial Functions and Applications

Global Optimization of Polynomial Functions and Applications by Jiawang Nie Doctor of Philosophy in Applied Mathematics University of California, Berkeley Professor James Demmel, Co-Chair Professor Bernd Sturmfels, Co-Chair This thesis discusses the global optimization problem whose objective function and constraints are all described by (multivariate) polynomials. The motivation is to find the...

Growth Estimates for Exp-Log Functions

Exp-log functions are those obtained from the constant 1 and the variable X by means of arithmetic operations and the function symbols exp() and logll. This paper gives an explicit algorithm for determining eventual dominance of these functions modulo an oracle for deciding zero equivalence of constant terms. This also provides another proof that the dominance problem for exp-log functions is T...

Global Optimization of Costly Nonconvex Functions, with Financial Applications

Twofold exp and log

This article is about twofold arithmetic [1, 2]. Here I introduce algorithms and experimental code for twofold variant of C/C++ standard functions exp() and log(), and expm1() and log1p(). Twofold function y0 + y1 ≈ f(x0 + x1) is nearly 2x-precise so can assess accuracy of standard one. Performance allows assessing on-fly: twofold texp() over double is ~10x times faster than expq() by GNU quadm...