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15
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Lexicographic ordering

Published on
#discrete-mathematics #convex-analysis #convex-optimization
32
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Proof for convexity of a fractional function

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#convex-analysis #convex-optimization
51
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Alternating Direction Method of Multipliers (ADMM) special case

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#optimization #algorithms #convex-optimization
1k
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Minimizer of a convex function.

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#convex-analysis #convex-optimization
88
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Strict convexity of the norm

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#convex-analysis #convex-optimization
326
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Difference between objective function values of any feasible solution and optimal solution

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#optimization #convex-analysis #convex-optimization #least-squares
435
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Square LP. Consider the LP with $A$ square and nonsingular. Minimize $c^Tx$.

Published on
#optimization #convex-optimization #linear-programming
55
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Proof of ADMM special case

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#optimization #algorithms #convex-optimization
49
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Calculating whether infimum optimization problem is convex

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#optimization #convex-optimization
80
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Maximising $Tr(PAPB)$ for orthogonal projection matrix $P$ and symmetric $A,B$.

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#linear-algebra #eigenvalues-eigenvectors #convex-optimization #trace
98
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Convexity of abs of quadratic form

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#convex-analysis #convex-optimization #quadratic-forms
41
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$\min_{\beta_1,...,\beta_3,\beta}\sum_{i=1}^{3}\frac{1}{2}||y_i-X_i\beta_i||_2^2+\lambda||\beta||_1$ in augmented Lagrangian form

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#optimization #convex-optimization #lagrange-multiplier
41
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Basic result on convex sets

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#convex-analysis #convex-optimization #convex-geometry
65
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Prove that, for $f(x), g(x)$ convex, $\alpha_f f(x) + \alpha_g g(x)$ is also convex for $x ∈ S \subset \mathbb R^n$ where $\alpha_f, \alpha_g\ge0$.

Published on
#optimization #convex-analysis #convex-optimization #convex-geometry
129
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Which is stronger, Kurdyka-Łojasiewicz property or regular? If the comparison is not proper, what are their range of applications?

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#optimization #convex-optimization #non-convex-optimization #subgradient #non-smooth-analysis

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