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Optimization is the mathematical problem of finding a decision to achieve the best possible outcome while satisfying certain restrictions. Linear programs, conic linear programs and discrete optimization problems arise in a myriad of applications: electricity markets, airlines, logistics, public transport, international shipping, mining, finance, engineering, and data science.?This course will provide an introduction to the basic mathematical theory, modelling techniques, computational methods and selected applications of linear, conic and discrete optimization.

这是一份unsw新南威尔士大学MATH3171 的成功案例

线性和离散优化模型|MATH3171 Linear and Discrete Optimization Modelling

问题 1.

Let H be a weakly cancellative d-monoid with ordinal decomposition (Hλ,λ∈Λ) left( mathrm{H}{ lambda}, lambda in Lambda right). (1) If λ(a)≤min(λ(b),λ(c)) lambda(a) leq min ( lambda(b), lambda(c)) then a?b=a?ca * b=a * c implies b == c. (2) If λ(a)≤min(λ(b),λ(c)) lambda(a) leq min ( lambda(b), lambda(c)) and d≤ad leq a then a abd≠ca b d neq c implies b ≤ leq c. (3) For a n holds then cancellation leads to the contradiction a >b>b. Otherwise λ(b?c)≤λ(a?c) lambda(b * c) leq lambda(a * c). On the other hand a?c0 alpha>0 and a >b.AsR+?Q+> mathrm{b} . mathrm{As} mathrm{R}{+} subset mathrm{Q}{+}we find α=n/m alpha=n / m for some m,n∈Nm, n in mathbb{N} with greatest common divisor 1. Therefore there exist p,q∈Zp, q in Z with pn +qm=1.+q m=1 . This 1mp1q1 mathrm{mp} 1 mathrm{q}.1/m=p(n/m)+q∈R+? 1 / m=p(n / m)+q in R_{+} cdot Let a′=(1/m)a^{ prime}=(1 / m) a and b′=(1/m)b^{ prime}=(1 / m) a . Now a