Questions tagged [convexity]

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

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17 votes
5 answers

Linear Programming with additional "if-then"/"Default to zero" constraints?

What approaches can I use for a Linear Programming problem with the additional constraint that if a decision variable falls below a certain threshold, then it should just be forced to 0. I'm ...
Skander H.'s user avatar
  • 2,139
12 votes
2 answers

Convex vs Strictly Quasiconvex Functions in Optimization

I have read/heard quite a few time that in the old days, it was considered that linear programs constitute the class of optimization problems that can be solved efficiently in practice (as a rule of ...
user2316602's user avatar
12 votes
2 answers

Dedicated solver for convex problems

Are you aware of a fast solver (open source or commercial) for convex NLPs that is faster than IPOPT? I'm interested in problems in the 50K+ variable range, both dense and sparse. Ideally, it would be ...
Nikos Kazazakis's user avatar
12 votes
1 answer

Recovering primal optimal solutions from dual sub gradient ascent using ergodic primal sequences

My question concerns recovering a primal optimal solution while performing dual sub gradient ascent. Denoting by $y_i$ the dual multiplier in the $i^{\text{th}}$ iteration, let \begin{equation} x_i = ...
batwing's user avatar
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12 votes
2 answers

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 ...
independentvariable's user avatar
7 votes
2 answers

How can I linearize or convexify this binary quadratic optimization problem?

I have an optimization problem as below. I am having a hard time with the last constraint. $\max \eta$ subject to ${\bf U}(:,m)^T{\bf A}{\bf U}(:,m)=0,m=1,2,\cdots,M$ here $\bf{A}$ is a Binary ...
KGM's user avatar
  • 2,211
3 votes
2 answers

How to make following constraint a convex one?

I would like to write a constraint as follows, where $x,y>0$ are optimization variables, and $a,b,c,d,A$ are positive constants. How to make it a convex constraint? \begin{equation} \frac{{ax}}{{\...
qinqinxiaoguai's user avatar