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Optimization deals with selecting the simplest option among a number of possible choices that are feasible or do not violate constraints. Python is used to optimize parameters in a model to best fit data, increase profitability of a possible engineering style, or meet another form of objective which will be described mathematically with variables and equations.


pyOpt is a Python-based package for formulating and solving nonlinear constrained optimization problems in an efficient, reusable and portable manner. Python programming uses object-oriented concepts, such as class inheritance and operator overloading, to maintain a distinct separation between the problem formulation and the optimization approach used to solve the problem.


All optimisation downside solvers inherit from the Optimizer abstract category. The category attributes include the solver name (name), an optimizer kind symbol (category), and dictionaries that contain the solver setup parameters (options) and message output settings (informs). The class provides ways to check and alter default solver parameters (getOption, setOption), as well as a method that runs the solver for a given optimisation problem (solve).


Optimization solver

A number of constrained optimization solvers are designed to solve the general nonlinear optimization problem.

  1. PSQP: This optimizer is a preconditioned sequential quadratic programming algorithm. This optimizer implements a sequential quadratic programming method with a BFGS variable metric update.
  2. SLSQP: This optimizer is a sequential least squares programming algorithm. SLSQP uses the Han–Powell quasi-Newton method with a BFGS update of the B-matrix and an L1-test function in the step-length algorithm. The optimizer uses a slightly modified version of Lawson and Hanson’s NNLS nonlinear least-squares solver.
  3. CONMIN: This optimizer implements the method of feasible directions. CONMIN solves the nonlinear programming problem by moving from one feasible point to an improved one by choosing at each iteration a feasible direction and step size that improves the objective function.
  4. COBYLA: It is an implementation of Powell’s nonlinear derivative–free constrained optimization that uses a linear approximation approach. The algorithm is a sequential trust–region algorithm that employs linear approximations to the objective and constraint functions.
  5. SOLVOPT: SOLVOPT is a modified version of Shor’s r–algorithm with space dilation to find a local minimum of nonlinear and non–smooth problems.
  6. KSOPT: This code reformulates the constrained problem into an unconstrained one using a composite Kreisselmeier–Steinhauser objective function to create an envelope of the objective function and set of constraints. The envelope function is then optimized using a sequential unconstrained minimization technique.
  7. NSGA2: This optimizer is a non-dominating sorting genetic algorithm that solves non-convex and non-smooth single and multiobjective optimization problems.
  8. ALGENCAN: It solves the general non-linear constrained optimization problem without resorting to the use of matrix manipulations. It uses instead an Augmented Lagrangian approach which is able to solve extremely large problems with moderate computer time.
  9. FILTERSD: It use of a Ritz values approach Linear Constraint Problem solver. Second derivatives and storage of an approximate reduced Hessian matrix is avoided using a limited memory spectral gradient approach based on Ritz values.


To solve an optimization problem with pyOpt an optimizer must be initialized. The initialization of one or more optimizers is independent of the initialization of any number of optimization problems. To initialize SLSQP, which is an open-source, sequential least squares programming algorithm that comes as part of the pyOpt package, use:

>>> slsqp = pyOpt.SLSQP()

This initializes an instance of SLSQP with the default options. The setOption method can be used to change any optimizer specific option, for example the internal output flag of SLSQP:

>>> slsqp.setOption('IPRINT', -1)

Now Schittkowski’s constrained problem can be solved using SLSQP and for example, pyOpt’s automatic finite difference for the gradients:

>>> [fstr, xstr, inform] = slsqp(opt_prob,sens_type='FD')

By default, the solution information of an optimizer is also stored in the specific optimization problem. To output solution to the screen one can use:

>>> print opt_prob.solution(0)



The problem is taken from the set of nonlinear programming examples by Hock and Schittkowski and it is defined as


      min            − x1x2x3



subjected to     x1 + 2x2 + 2x3 − 72 ≤ 0

                        − x1 − 2x2 − 2x3 ≤ 0


                        0 ≤ x1 ≤ 42

                        0 ≤ x2 ≤ 42

                        0 ≤ x3 ≤ 42


The optimum of this problem is at (x1∗ , x2∗ , x3* ) = (24, 12, 12), with an objective function value of f ∗ = −3456, and constraint values g (x∗ ) = (0, −72).



# Standard Python modules


import os, sys, time

import pdb


# Extension modules


#from pyOpt import *

from pyOpt import Optimization

from pyOpt import PSQP

from pyOpt import SLSQP

from pyOpt import CONMIN

from pyOpt import COBYLA

from pyOpt import SOLVOPT

from pyOpt import KSOPT

from pyOpt import NSGA2

from pyOpt import ALGENCAN

from pyOpt import FILTERSD



def objfunc(x):


    f = -x[0]*x[1]*x[2]

    g = [0.0]*2

    g[0] = x[0] + 2.*x[1] + 2.*x[2] - 72.0

    g[1] = -x[0] - 2.*x[1] - 2.*x[2]


    fail = 0

    return f,g, fail  



# Instantiate Optimization Problem

opt_prob = Optimization('Hock and Schittkowski Constrained Problem',objfunc)







print opt_prob


# Instantiate Optimizer (PSQP) & Solve Problem

psqp = PSQP()



print opt_prob.solution(0)


# Instantiate Optimizer (SLSQP) & Solve Problem

slsqp = SLSQP()



print opt_prob.solution(1)


# Instantiate Optimizer (CONMIN) & Solve Problem

conmin = CONMIN()



print opt_prob.solution(2)


# Instantiate Optimizer (COBYLA) & Solve Problem

cobyla = COBYLA()



print opt_prob.solution(3)


# Instantiate Optimizer (SOLVOPT) & Solve Problem

solvopt = SOLVOPT()



print opt_prob.solution(4)


# Instantiate Optimizer (KSOPT) & Solve Problem

ksopt = KSOPT()



print opt_prob.solution(5)


# Instantiate Optimizer (NSGA2) & Solve Problem

nsga2 = NSGA2()



print opt_prob.solution(6)


# Instantiate Optimizer (ALGENCAN) & Solve Problem

algencan = ALGENCAN()



print opt_prob.solution(7)


# Instantiate Optimizer (FILTERSD) & Solve Problem

filtersd = FILTERSD()



print opt_prob.solution(8)


Solving non-linear global optimization problems could be tedious task sometimes. If the problem is not that complex then general purpose solvers could work. However, as the complexity of problem increases, general purpose global optimizers start to take time. That is when need to create your problem specific fast and direct global optimizer’s need arises.


We have an specialized team with PHD holders and coders to design and develop customized global optimizers. If you need help with one, please feel free to send your queries to us.


We first understand the problem and data by visualizing it. After that we create a solution to your needs.


Please do read to understand what a solver is and how it works - If you want to create your own simple solver. This is not exactly how every solver works, however, this will give you a pretty solid idea of what is a solver and how it is supposed to work.

NLP is a branch of data science that consists of systematic processes for analyzing, understanding, and deriving information from the text information in a smart and efficient manner. By utilizing NLP and its parts, one can organize the massive chunks of text information, perform various automated tasks and solve a wide range of issues like – automatic summarization, machine translation, named entity recognition, relationship extraction, sentiment analysis, speech recognition, and topic segmentation etc.


NLTK (Natural Language Toolkit) is a leading platform for building Python programs to work with human language data. It provides easy-to-use interfaces to lexical resources like WordNet, along with a collection of text processing libraries for classification, tokenization, stemming, and tagging, parsing, and semantic reasoning, wrappers for industrial-strength NLP libraries.


NLTK has been called “a wonderful tool for teaching and working in, computational linguistics using Python,” and “an amazing library to play with natural language.”


Downloading and installing NLTK

  1. Install NLTK: run pip install nltk
  2. Test installation: run python then type import nltk and run nltk.download() and download all packages.


Pre-Processing with NLTK

The main issue with text data is that it's all in text format. However, the Machine learning algorithms need some variety of numerical feature vector so as to perform the task. Thus before we have a tendency to begin with any NLP project we'd like to pre-process it to form it ideal for working. Basic text pre-processing includes:


  • Converting the whole text into uppercase or lowercase, in order that the algorithm doesn't treat the same words completely different in several cases.
  • Tokenization: Process of converting the normal text strings into a list of tokens i.e. words that we actually want. The NLTK data package includes a pre-trained Punkt tokenizer for English.


           import nltk

           from nltk.tokenize import word_tokenize

           text = "God is Great! I won a lottery."


           Output: ['God', 'is', 'Great', '!', 'I', 'won', 'a', 'lottery', '.']


  • Noise removal: Process of removing everything that isn’t in a standard number or letter.
  • Stop word removal: A stop word is a commonly used word (such as “the”, “a”, “an”, “in”). We would not want these words or taking up valuable processing time. For this, we can remove them easily, by storing a list of words that you consider to be stop words. NLTK (Natural Language Toolkit) in python has a list of stopwords stored in sixteen different languages. You can find them in the nltk_data directory.  home/Saad/nltk_data/corpora/stopwords is the directory address.

           import nltk

           from nltk.corpus import stopwords



  • Stemming: Stemming is the process of reducing the words to its root form. Example if we were to stem the following words: “Connects”, “Connecting”, “Connected”, “and Connection”, the result would be a single word “Connect”.

           # import these modules

           from nltk.stem import PorterStemmer

           from nltk.tokenize import word_tokenize   

           ps = PorterStemmer()  

           # choose some words to be stemmed

           words = ["Connect", "Connects", “Connected”, "Connecting", "Connection", "Connections"]


           for w in words:

           print(w, " : ", ps.stem(w)) 


  • Lemmatization: Lemmatization is the process of grouping along the various inflected forms of a word in order that they may be analyzed as a single item. Lemmatization is similar to stemming but it brings context to the words. Therefore it links words with similar meaning to one word.

           # import these modules

           from nltk.stem import WordNetLemmatizer  

           lemmatizer = WordNetLemmatizer()  

           print("rocks :", lemmatizer.lemmatize("rocks"))

           print("corpora :", lemmatizer.lemmatize("corpora"))  

           # a denotes adjective in "pos"

          print("better :", lemmatizer.lemmatize("better", pos ="a"))


          -> rocks : rock

          -> corpora : corpus

          -> better : good


Now we need to transform text into a meaningful vector array. This vector array is a representation of text that describes the occurrence of words within a document. For example, if our dictionary contains the words {Learning, is, the, not, great}, and we want to vectorize the text “Learning is great”, we would have the following vector: (1, 1, 0, 0, 1). A problem is that extremely frequent words begin to dominate within the document (e.g. larger score), however might not contain as much informational content. Also, it will offer additional weight to longer documents than shorter documents.


One approach is to rescale the frequency of words or the scores for frequent words called Term Frequency-Inverse Document Frequency.


  • Term Frequency: is a scoring of the frequency of the word in the current document.

           TF = (Number of times term t appears in a document)/ (Number of terms in the document)


  • Inverse Document Frequency: It is a scoring of how rare the word is across documents.

           IDF = 1+log(N/n), where, N is the number of documents and n is the number of documents a term t has appeared in.


           Tf-idf weight is a weight often used in information retrieval and text mining.

           Tf-IDF can be implemented in scikit learn as:


           from sklearn.feature_extraction.text import TfidfVectorizer

           corpus = [

           ...     'This is the first document.’

           ...     'This document is the second document.’

           ...     'And this is the third one.’

           ...     'Is this the first document?',]

           >>> vectorizer = TfidfVectorizer()

           >>> X = vectorizer.fit_transform(corpus)

           >>> print(vectorizer.get_feature_names())

           ['and', 'document', 'first', 'is', 'one', 'second', 'the', 'third', 'this']

           >>> print(X.shape)

           (4, 9)


  • Cosine similarity: TF-IDF is a transformation applied to texts to get two real-valued vectors in vector space. We can then obtain the Cosine similarity of any pair of vectors by taking their dot product and dividing that by the product of their norms. That yields the cosine of the angle between the vectors. Cosine similarity is a measure of similarity between two non-zero vectors.

           Cosine Similarity (d1, d2) =  Dot product(d1, d2) / ||d1|| * ||d2||


          import numpy as np

          from sklearn.metrics.pairwise import cosine_similarity

          # vectors

          a = np.array([1,2,3])

          b = np.array([1,1,4])

          # manually compute cosine similarity

          dot = np.dot(a, b)

          norma = np.linalg.norm(a)

          normb = np.linalg.norm(b)

          cos = dot / (norma * normb)


After completion of cosine similarity matric we perform algorithmic operation on it for Document similarity calculation, sentiment analysis, topic segmentation etc.


I have done my best to make the article simple and interesting for you, hope you found it useful and interesting too.

In every era, marketing has evolved based on what the customer is using. If you go back in history, you can see that at times when customers used Radio, it gave birth to radio advertising and marketing. Next, we got the boom of televisions, it is one of the widely used device globally, which allowed the companies to reach a mass audience with TV ads. Even today TV advertising is one of the most used advertising strategies for companies. Since the boom of the Internet, more customers started using the Internet, which gave birth to a new era of marketing originally called Internet marketing, which is now called Digital Marketing.


Now a days, we frequently hear the term Digital marketing we all think that we reasonably understand what actually it is. This thinking sometimes limits the scope and opportunity that the complete Digital marketing landscape will actually offer, which is why, when it involves nailing it down, we either turn dumbfounded or get stuck. To come out of such scenarios, it is important to know different types of Digital marketing opportunities that are available to your business. According to Salesforce, 75th of Total marketing Budget will head to Digital marketing.


Digital marketing depends upon the kinds of audience interactions. It revolves around managing and harnessing of various types of Digital marketing Channels and many varieties of Digital marketing services.


Digital marketing encompasses all marketing efforts that use an electronic device or the internet. Businesses leverage digital channels like search engines, social media, email, and their websites to connect with current and prospective customers.

Why companies use digital marketing?

  1. Internet Users: As per the internet usage stats, 40% of the world population is using the internet.
  2. Mobile Phones: Most of the users globally today use mobile phones for communication. As per a report 4.77 billion mobiles phone users globally, which will increase to 5.07 billion by 2019.
  3. Targeting the Audience: In traditional marketing strategies, it is very difficult to advertise to the target audience with specific demographics & details. Today with digital marketing we have so many customised & personalised methods to target the audience exclusively.
  4. Low Cost and High ROI: Most of the small and medium scale companies rely mostly on digital marketing strategies due to its low cost and high return on investment.

Digital Marketing Types

  1. Search Engine Optimisation: SEO is the process of optimising your website to "rank" higher in search engine results pages, thereby increasing the amount of organic (or free) traffic your website receives. The channels that benefit from SEO include Website, Blogs or Info-graphics.
  2. Content Marketing: CM denotes the creation and promotion of content assets for the purpose of generating brand awareness, traffic growth, lead generation, and customers. The channels that can play a part in your content marketing strategy include Blogs posts, Ebooks and whitepaper, info-graphics, online brochures and look-books.
  3. Social Media Marketing: SMM promotes your brand and your content on social media channels to increase brand awareness, drive traffic, and generate leads for your business. The channels you can use in social media marketing include Facebook, Twitter, Instagram, linked In, Snap-chat, or google+.
  4. Pay-Per-Click: PPC is a method of driving traffic to your website by paying a publisher every time your ad is clicked. One of the most common types of PPC is Google AdWords, which allows you to pay for top slots on Google's search engine results pages at a price "per click" of the links you place. Other channels where you can use PPC include Paid ads on Facebook, Promoted Tweets on Twitter.
  5. Email Marketing: Companies use email marketing as a way of communicating with their audiences. Email is often used to promote content, discounts and events, as well as to direct people toward the business's website.

Digital Marketing Strategies

Here is a list of five simple digital marketing strategies that any business owner can implement to help their business grow:

  1. Setting a goal: Digital marketing is a great way for small businesses to prosper, but going into the method blindly can leave you with a jumbled mess. A lot of strategy and precision goes into digital marketing and having a goal helps you recognise what to focus on.
  2. Creating a Marketing Funnel: The most successful businesses have a good marketing funnel in place. A marketing funnel is when you map out a customer’s journey from when a customer is a complete stranger to once they become a lead, then put certain methods in place that may encourage them to move through this funnel. Things like lead magnets, calls to action, opt-ins and offers are all effective pieces of a funnel. You’ll consider a marketing funnel in four parts: Awareness, Interest, Desire, and Action.
  3. Developing a call-to-action: A call-to-action (CTA) is a picture or text that prompts visitors to take action, like subscribe to a newsletter, read a webinar or request a product demo. CTAs should direct people to landing pages, wherever you'll collect visitors’ contact info in exchange for a valuable marketing offer. In that sense, an effective CTA results in more leads and conversions for your web site. This path, from a click on a CTA to a landing page, illustrates a lot of desired process of lead generation.
  4. Creating an Effective Lead magnet: The idea behind a lead magnet is to trade information. You supply something like a free download of a white paper, but in order to complete the download the individual has to fill out a form that will provide you with more information about them. You’ll use the information you gather to interact with them more as they progress through your funnel.
  5. Driving Traffic: There a variety of ways you can drive traffic to your website.
  • Quality Content: Use content like blog posts, press releases and articles on authority websites. Insert links to various places on your web site inside this content to create your brand name through exposure and drive traffic to your website.
  • Keyword Strategy: Inserting related keywords into content will help your content and website show up in more search results, this leads to higher volumes of web traffic.
  • Website Optimisation: Ensuring that your website is optimised and functioning at its best is essential. People don’t want to visit a website that doesn’t work properly.
  • Social Media: Use engaging social media posts to attract more traffic to your site. Using pictures, video, and other relevant media will help your posts get more engagement.


We have many different specialisations so you will have different options to start your career.

  1. Digital marketing strategist
  2. Digital marketing executive
  3. SEO analyst
  4. Social media specialist
  5. Google AdWords specialist
  6. Email marketing specialist
  7. Web Analyst
  8. Online reputation manager

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