2
votes
1answer
42 views

Origin of Slater's condition

I've been looking all over the internet to answer this question: Slater's condition is a commonly used to certify that strong duality holds in a convex optimization problem. Although used in many ...
2
votes
1answer
54 views

Got stuck with this $L^2(-1, 1)$ optimization problem. Any ideas where it comes from?

Statement Let $u(x) \in L^2(-1, 1)$. Solve the following optimization problem: $$ \begin{cases} J(u) = 4 \int_{-1}^{1} \sqrt{|x| (1 - |x|)} u(x) dx + \left(\int_{-1}^1 \sin(3\pi x) u(x) dx\right)^2 ...
0
votes
0answers
44 views

optimization problem in mathmetical finance using convex duality

I'm interested in the application of stochastic processes and stochastic calculus in mathematical finance. In my lecture I often see a certain optimization problem usually of a convex function. ...
0
votes
1answer
48 views

Constrained optimization with complex variables

Is there a theory of constrained optimization with complex variables, do you know any textbook on that topic? The typical textbooks on constrained optimization deal with real variables. I actually ...
1
vote
0answers
37 views

Is there a textbook treatment of Ky Fan's minimax theorem and its generalizations?

Theorem 2 in Ky Fan(1952) is a powerful tool in zero-sum games, which states: Let $X$ be a compact Hausdorff space and $Y$ an arbitary set (not topologized). Let $f$ be a real-valued function on ...
1
vote
1answer
21 views

References or texts for learning about the augmented lagrangian?

I am reading a paper about a convex model for non-negative matrix factorization. In the paper it describes how to do such a technique and it says that it uses the augmented Lagrangian. I can't find ...
0
votes
0answers
54 views

References for maximizing a product under a sum equality constraint and individual variable inequality constraints

I am looking for references on the following optimization problem: maximize $\prod x_i$ under a sum constraint $\sum x_i = 1$ and individual variable constraints $0 \le x_i \le C_i$. I know the ...
1
vote
2answers
66 views

Absract convergence of a suboptimal version of steepest descent

I'm looking for a citable reference to fill in a gap in an intermediate step of a proof which requires convergence of a suboptimal version of steepest descent. The function $f:\bf{R}^n\to\bf{R}^n$ I ...
0
votes
1answer
48 views

A reference to learn about duality

I am interested in learning about duality in convex optimization. I am looking for something to read which is: Reasonably short. Fairly self-contained (if it is a chapter in a textbook, I would ...
1
vote
0answers
54 views

Suggestions for a reference-level text on optimization theory?

I'd be interested in knowing if anybody has suggestions on an advanced but still self-contained reference on optimization theory, centered around linear and convex problems. The key feature of my ...
1
vote
0answers
21 views

I need a resource for basic convex optimization algorithms.

I'm trying to decide whether or not a certain CS problem can be solved in polynomial time. I've got it reduced down to a basic convex optimization problem, but I can't for the life of me find a good ...
1
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0answers
34 views

Basic questions about convex optimization

I have some basic questions about convex optimization. From finding sources online, I've seen that many algorithms (for example, Newton's method) describe themselves as $o(\frac{1}{\epsilon})$. ...
0
votes
1answer
46 views

Degeneracy of the analytic center of a set of linear inequalities

I have a question about the degeneracy of the analytic center of a set of linear inequalities. When the set of linear inequalities is degenerate, I guess that the analytic center would also be ...
3
votes
1answer
56 views

Convex programming when the problem has an underlying combinatorial structure that's a DAG

I have a nonlinear convex objective function to minimize. The function is defined on a set of variables: $\{ x_1,x_2, \ldots ,x_p \},$ where each $x_i$ is a number associated with a path in the DAG. ...
1
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0answers
235 views

A convex programming problem involving sum of logarithms of linear functions

Here is a convex programming problem I encountered while working on an estimation problem for a mixture of multinomial distributions. We have a matrix $A_{m \times n}$ containing non-negative real ...