Convex optimization unique solution

  • Does a quadratic program have a unique solution?

    For an unconstrained quadratic problem it is intuitive, based on convexity, that the optimum is unique.
    For an equality constrained problem, one can express the optimal solution in terms of the KKT system of equations, which has a unique solution..

  • Therefore, every optimization problem has a well-defined optimal value.
    But not every optimiza- tion problem has an optimal solution.
    For example, consider the optimization problem min {ex : x ∈ R}. this problem has an optimal value of zero, but there is no optimal solution.
Sep 13, 2016There is a statement in a thesis I am reading, The solution of a convex optimization problem is unique, and the global and the local minima are  When does an optimization problem have a unique solution, no Is a global optimal solution of a convex problem always unique?Unique solution of convex problem - Mathematics Stack ExchangeOptimization under constraints - unique solution or notMore results from math.stackexchange.com
Sep 13, 2016There is a statement in a thesis I am reading, The solution of a convex optimization problem is unique, and the global and the local minima are  When does an optimization problem have a unique solution, no Optimization under constraints - unique solution or notUnique solution of convex problem - Mathematics Stack ExchangeIs a global optimal solution of a convex problem always unique?More results from math.stackexchange.com

Can a convex optimization function be self-concordant?

In practice, algorithms do not set the value of so aggressively, and update the value of a few times

For a large class of convex optimization problems, the function is self-concordant, so that we can safely apply Newton's method to the minimization of the above function

Is the solution of a convex optimization problem unique?

There is a statement in a thesis I am reading, The solution of a convex optimization problem is unique, and the global and the local minima are essentially the same

Is there a proof for it?

What if RF(X) = 0 is a convex function?

The theorem states that for convex problems, rf(x) = 0 is not only necessary, but also su cient for local and global optimality

cient even for local optimality (e g , think of f(x) = x3 and x = 0) 0

Note that a convex function automatically passes this test

Recall that a fuction f : Rn ! R is strictly convex if 8x; y; x 6 = y; 8 2 (0; 1),

Convex optimization problems do not have unique solutions. You need strict convexity for that.

Categories

Convex optimization upenn
Convex optimization uoft
Convex optimization uw
Convex optimization ubc
Convex optimization unipd
Convex optimization ucla
Convex optimization ucsd
Convex optimization udemy
Convex optimization umd
Convex optimization using matlab
Convex optimization vs non convex
Convex optimization vs linear programming
Convex optimization video lectures
Convex optimization visualization
Convex optimization variable splitting
Convex vector optimization
Convex vector optimization problem
Convex optimal value function
Private convex optimization via exponential mechanism
Convex optimization slack variables