# Questions tagged [convexity]

For questions related to convex functions and convex sets, especially as they relate to optimization problems.

48 questions
Filter by
Sorted by
Tagged with
1 vote
98 views

### Convex not strictly convex!

Update: Linear programming problems (LP) have a convex space, precisely vector space, such as a convex feasible region as pointed out by @prubin. Also, they may have either unique or multiple ...
• 6,206
45 views

### FOC point vs Stationary point in local optimization

In this SIAM Review paper the authors are giving the following necessary condition for a point being a local maximum of a convex function: Let $F: \mathbb{R}^n \mapsto \mathbb{R}$ be convex. If $x$ ...
• 3,786
86 views

• 111
1 vote
76 views

### Find a dual problem with one dual decision variable to the problem of finding the orthogonal projection of a given vector

Given the set $T_{\alpha}=\{x\in\mathbb{R}^n:\sum x_i=1,0\leq x_i\leq \alpha\}$ For which $\alpha$ the set is non-empty? Find a dual problem with one dual decision variable to the problem of finding ...
• 395
101 views

• 381
198 views

241 views

### Solving convex programs defined by separation oracles?

General question: What software can solve convex programs defined by a separation oracle? The objective function is concave, and the feasible set is a polytope. By a separation oracle I mean that I ...
• 203
1k views

### Is This Constraint Convex?

I have a constraint that I believe to be convex and not affine which I think means that I can implement a relaxation. I will first define the full constraint, and then build up my (informal) reasoning ...
• 2,259
396 views

### Convexity of a QP

In quadratic programming (QP), you encounter an objective of the following form: $$x^TQx + c^Tx$$ and often it's desirable to know if the QP is convex. One method to check for convexity is by ...
• 705
653 views

• 1,589
934 views

### Convex Maximization with Linear Constraints

I am doing active research in convex maximization w.r.t. linear constraints. There are many cases which can be efficiently approximately solved, e.g., convex quadratic maximization, log-sum-exp ...
• 3,786
It is well known that expectation preserves convexity: If $f(x)$ is convex and $Y$ is a random variable, then $\mathbb E[f(x-Y)]$ is convex. This property arises in, for example, inventory theory. I ...