Questions tagged [convex-optimization]

Convex optimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. The convexity property can make optimization in some sense "easier" than the general case - for example, any local minimum must be a global minimum.

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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 ...
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What is the best open source solver for large scale LP optimization in pyomo?

I have used Gurobi and cplex for solving large scale LP problems with Pyomo. However, I do need to use open source solver. Any advise? glpk and cbc seems to be very slow in solving the problem (with ...
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Maximize correlation subject to nonconvex correlation constraints

Let $r, z$ and each of $u_i$ be a length $n$ vector. I’d like to maximize the correlation between $z$ and $r$ (when that correlation is positive) while keeping $z$ “away” from $u_i$’s. Formally, \...
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Convex Optimization: Separation of Cones

I am trying to solve Exercise 2.39 at Boyd and Vandenberghe's Convex Optimization book. In one source, the answer is given as: 2.39 Separation of cones. Let $K$ and $\tilde K$ be two convex cones ...
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Why does some solvers can only solve conic optimization problems?

Famous solvers like sedumi, sdpt3, mosek can solve conic optimization, but not more general convex optimization. Why? I know many convex problems can be formulated as conic, but still confused.
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