Convex optimization introduction

  • What is the introduction of convex set?

    A convex set is a collection of points in which the line AB connecting any two points A, B in the set lies completely within the set.
    In other words, A subset S of En is considered to be convex if any linear combination θx1 + (1 − θ)x2, (0 ≤ θ ≤ 1) is also included in S for all pairs of x1, x2 ∈ S..

  • Why is convex optimization important?

    Convex optimization has become an essential tool in machine learning because many real-world problems can be modeled as convex optimization problems.
    For example, in classification problems, the goal is to find the best hyperplane that separates the data points into different classes..

This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications,  Lecture NotesSyllabusAssignmentsReadings
Convex optimization refers to the minimization of a convex objective function subject to convex constraints. Convex opti- mization techniques are important in engineering applications because a local optimum is also a global optimum in a convex problem and a rigorous optimality condition and a duality theory exist to verify the optimal solution.

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