An Effective Method for Globally Solving a Class of Multiplicative Problems

2010 ◽  
Author(s):  
Yun-Rui Guo ◽  
Hong-Wei Jiao
Keyword(s):  
Multiplicative Problems

Optimization Method for Globally Solving a Kind of Multiplicative Problems with Coefficients

2011 ◽  
Vol 467-469 ◽  
pp. 526-530 ◽  
Author(s):  
Hong Wei Jiao ◽  
Jing Ben Yin ◽  
Yun Rui Guo
Keyword(s):  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Linearization Method ◽  
Equivalent Transformation ◽  
Engineering System ◽  
Linear Programming Problems ◽  
Global Optimal ◽  
Multiplicative Problems

Multiplicative problems are a kind of difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, system, finance, economics, and other fields. In this paper, an optimization method is proposed to globally solve a class of multiplicative problems with coefficients. Firstly, by utilizing equivalent transformation and linearization method, a linear relaxation programming problem is established. Secondly, by using branch and bound technique, a determined algorithm is proposed for solving equivalent problem. Finally, the proposed algorithm is convergent to the global optimal solution of original problem by means of the subsequent solutions of a series of linear programming problems.

Approximation of linear fractional-multiplicative problems

2009 ◽  
Vol 128 (1-2) ◽  
pp. 437-443 ◽  
Author(s):  
Daniele Depetrini ◽  
Marco Locatelli
Keyword(s):  
Multiplicative Problems

scholarly journals Multiplicative Gains, Non-ergodic Utility, and the Just One More Paradox (with Supplemental Information)

2021 ◽  
Author(s):  
John K. Myers
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Expected Value ◽  
Multiplicative Semigroup ◽  
The Real ◽  
Operator Notation ◽  
Multiplicative Problems ◽  
Utility Preferences ◽  
Continuous Operators

Abstract Interest in multiplicative vs. additive returns on bets has been revived by Peters, who proposes ergodicity and added noise are useful in understanding utility preferences. Peters requires a Monte Carlo simulation to demonstrate empirically a supposed paradox that arithmetic expectation is inappropriate for multiplicative gain distribution forecasting. Here I formalize the r operator notation, which significantly simplifies multiplicative problems, as an extension of the arithmetic group's Δ/d discrete and continuous operators into the multiplicative semigroup. I show how the annihilating (absorbing) element of the multiplicative semigroup at 0, not +/-∞, may be used to conveniently represent nonlinear sequence occurrences, such as running out of money, without the need for special computer rules outside the mathematics. I use this to solve Peters' expected-value paradox elegantly, without ergodicities nor noise. But Peters misses the real paradox, called “Just One More”: the outcome of an advantageous additive gamble is identical to the outcome of a similar disadvantageous multiplicative gamble, after one trial; hence, by induction, an agent will keep playing. I propose games “Hero or Heroin” and “American Roulette” to highlight this paradox. This may help in explaining addiction. The Supplement contains further visualizations and arguments against the need and applicability of ergodics for utility. The results contribute to the understanding of repeated multiplicative gambles with annihilating states, and their utility.

A FPTAS for a class of linear multiplicative problems

2007 ◽  
Vol 44 (2) ◽  
pp. 275-288 ◽  
Author(s):  
Daniele Depetrini ◽  
Marco Locatelli
Keyword(s):  
Multiplicative Problems
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