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Oct
10
comment Convex analysis books and self study.
@ZMI Are you talking about convex optimization or convex analysis? I am asking about convex analysis.
Sep
24
awarded  Autobiographer
Aug
30
accepted Uniqueness of symmetric positive definite matrix decomposition
Aug
24
awarded  Popular Question
Aug
21
comment Definition of Global Convergence
What is a considered a solution for a numerical optimization problem?
Aug
21
comment Definition of Global Convergence
I disagree. I believe what is regarded as solution is the Wikipedia page is a local solution. So global convergence does not worry about convergence to global optimum in the numerical optimization literature, but to a local optimum.
Aug
21
revised Definition of Global Convergence
edited tags
Aug
21
asked Definition of Global Convergence
Aug
10
comment Gradient descent (with line search) for convex functions viewed as alternation
Actually I see that $f$ is convex in terms of $D$ given a fixed $\alpha$, and $\alpha$ given a fixed $D$. However, I say it is not jointly convex in terms of the two variable together.
Aug
8
comment Gradient descent (with line search) for convex functions viewed as alternation
Does $a_t$ being there or not have anything to do with the solution of optimization problem in 2.1? (What is the difference between looking for a direction which is the best, or looking for a direction which multiplied by $a_t$ is the best?) Note that the coefficient $a_t$ is fixed in that problem.
Aug
8
revised $f$ is a linear function. If $f(x+3) + f(4x+5) = 10x$,$ f(x)=?$
Trying to increase readability
Aug
8
suggested suggested edit on $f$ is a linear function. If $f(x+3) + f(4x+5) = 10x$,$ f(x)=?$
Aug
8
revised Gradient descent (with line search) for convex functions viewed as alternation
edited title
Aug
8
comment Gradient descent (with line search) for convex functions viewed as alternation
I see! the source of confusion was that I used to think steepest direction comes from 2.1. Now I agree.
Aug
8
revised Gradient descent (with line search) for convex functions viewed as alternation
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Aug
8
revised Gradient descent (with line search) for convex functions viewed as alternation
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Aug
7
comment Gradient descent (with line search) for convex functions viewed as alternation
@ Michael Grant: In 2.1 I was trying to formalize "the direction of maximum decrease in function". After your question, I doubt that the steepest descent direction and the direction with maximum decrease in function value are the same or not. I see that one is talking about function and the other about directional derivative. (Should try to use Taylor's theorem to see). I am not sure yet. Thanks for mentioning this.
Aug
7
comment Gradient descent (with line search) for convex functions viewed as alternation
By the way, dear voters! It is not a good practice to vote for closing a question that contains some confusion, Especially when the goal of asking is specified as, resolving the confusion!
Aug
7
revised Gradient descent (with line search) for convex functions viewed as alternation
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Aug
7
comment Gradient descent (with line search) for convex functions viewed as alternation
Okay. You are right the algorithm is messed up here. I will correct it. But all I try to highlight and ask about is the non-joint-convexity of objective wrt search direction and step size in each iteration.