Optimization problem in standard formminimize f0(x)\text{minimize } f_0(x)minimize f0​(x)subject tofi(x)≤0,  i=1,…,mhi(x)=0,  i=1,…,pf_i(x) \le 0, \; i = 1, \dots, m \\ h_i(x) = 0, \; i = 1, \dots, pfi​(x)≤0,i=1,…,mhi​(x)=0,i=1,…,px∈Rnx\in \R^nx∈Rn is the optimization variablef0:Rn→Rf_0:\R^n\to \Rf0​:Rn→R is the objective or cost functionfi:Rn→R,  i=1,…,mf_i:\R^n\to \R, \; i = 1, \dots, mfi​:R..

Convex functionf:Rn→Rf:\R^n \to \Rf:Rn→R is convex if dom f\text{dom }f dom f is a convex set andf(θx+(1−θ)y)≤θf(x)+(1−θ)f(y)f(\theta x + (1 - \theta)y ) \le \theta f(x) + (1-\theta)f(y)f(θx+(1−θ)y)≤θf(x)+(1−θ)f(y)for all x,y∈dom f,0≤θ≤1x, y\in \text{dom }f, 0 \le\theta \le 1x,y∈dom f,0≤θ≤1fff is strictly convex if dom f\text{dom }fdom f is convex andf(θx+(1−θ)y)θf(x)+(1−θ)f(y)f(\theta x +..

Affine setLine : all points through x1,x2x_1, x_2x1​,x2​x=θx1+(1−θ)x2x = \theta x_1 + (1 - \theta) x_2x=θx1​+(1−θ)x2​where θ∈R\theta\in \Rθ∈RThis idea can be generalized to more than two points.θ1x1+θ2x2+⋯+θkxk\theta_1x_1 + \theta_2 x_2 + \cdots + \theta_kx_kθ1​x1​+θ2​x2​+⋯+θk​xk​where θ1+⋯+θk=1\theta_1 + \cdots + \theta_k = 1θ1​+⋯+θk​=1We refer to a point can be expressed as the following fo..

Mathematical optimizationmin⁡xfo(x)s.t fi(x)≤bi, i=1,…,m\begin{align}\min_x & f_o(x) \\ \text{s.t }& f_i(x) \le b_i, \ i = 1, \dots, m\end{align}xmin​s.t ​fo​(x)fi​(x)≤bi​, i=1,…,m​​wherex=(x1,…,xn)x = (x_1, \dots, x_n)x=(x1​,…,xn​): optimization variablesfo:Rn→Rf_o : R^n \to Rfo​:Rn→R: objective function (a.k.a the function we want to minimize)💡In deep learning or machine learning perspective..

Creating and Dropping usersTo create a user in MySQLUsername user can be followed by @ and the IP or the hostname from which the user is allowed to log in. Example:To drop a user: DROP USER userAuthorizationcontrol of what users can do in the database what they can see, create, modify, delete etcExercise 1What privileges are needed to be able to execute the following query?Answer:UPDATE (graduat..

IndexMotivationMySQL database, 10,000,000 peopleHow long does it take to find name and phone number for person with ID 4,857,845?How long does it take to find the phone number for all people named Kristin Elvik?The result of the second experiment is very slow. Why is it slow and what can we do about it?ExplanationThe slow query from the experiment performs a full table scan each row in the table..

Simple selectattribute : specifies a column in the resulttable_reference : the name of the tablewhere_condition : the condition that selected rows must satisfyExampleSelect DistinctTo remove duplicate rows from the result, we can use SELECT DISTINCTWhere ClauseLogical connections AND , OR , NOT can be used to create a more complex where conditionIS [NOT] NULLIS NULLIS NOT NULL💡NEVER use NULL nor..

Issues with DBMS DesignData integrity failure : e.g. key doesn’t exists💡앞 장에서 다룬 integrity constraint의 경우에는 위의 data integrity가 깨지지 않는 것을 보장하는 것이고, normalization은 data integrity가 보존되게끔 data base를 design한다는 의미라고 이해하면 된다.NormalizationThe process of breaking bad relations/tables smaller good relations→ leads to a better DB designAvoids updating, deleting, and inserting anomaliesThe normalization pro..