Hi, you can see these links:

The interior-point-convex algorithm:

http://www.mathworks.com/help/optim/ug/quadratic-programming-algorithms.html

Efficient Method of Solving Convex Hull:

http://www.mathworks.com/matlabcentral/answers/82229-efficient-method-of-solving-convex-hull-related-problem

This is a good question with many possible answers.

Computation of convex bodies using Matlab is covered in

http://www.mathworks.com/matlabcentral/fileexchange/43596-volume-computation-of-convex-bodies

This web page includes quite a number of Matlab scripts and functions to handle convexity.

Convex optimization (with Matlab in mind) is introduced in

J. Dattorro, Convex Optimization & Euclidean Distance Geometry, 2013:

https://ccrma.stanford.edu/~dattorro/0976401304.pdf

This book is a treasure-trove for those who are interested in using Matlab to solve convexity problems.    See, for example, Chapter 7, Proximity Problems, starting on page 567, where the term proximity means closeness in terms of distance.  Matlab scripts for this book are available on Wikimization:

http://www.mathworks.com/support/books/book49103.html?category=6&language=1&view=category

Hi, you can see these links:

The interior-point-convex algorithm:

http://www.mathworks.com/help/optim/ug/quadratic-programming-algorithms.html

Efficient Method of Solving Convex Hull:

http://www.mathworks.com/matlabcentral/answers/82229-efficient-method-of-solving-convex-hull-related-problem

Thank you Mostafa Eidiani & James F Peters 

Hi

dear mohamad , see the web

http://www.mathworks.com/support/books/book49103.html?category=6&language=1&view=category

Due to this question is very practical and good.

https://ccrma.stanford.edu/~dattorro/0976401304.pdf

Type 

help fmincon

in Matlab command window and Enter, and then learn about various algorithm available to solve convex optimization problems.

help fmincon

fmincon finds a constrained minimum of a function of several variables.

fmincon attempts to solve problems of the form:

min F(X) subject to: A*X