List questions from convex-analysis

641

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show the quadratic function $W(x_1,x_2,\ldots,x_n)=A\sum_{i} x_i^2+ \sum_{i\neq j} x_ix_j$ is quasi-concave

Published on 16 Apr 2026 - 21:14

3.5k

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Proof: A function is convex iff it is convex when restricted to any line ..

Published on 14 Apr 2026 - 19:26

884

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Concave optimization on closed unit ball, using penalty function

Published on 09 Apr 2026 - 10:39

1.2k

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Dual polyhedron & dual cone

Published on 12 Apr 2026 - 14:10

208

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Prove that $u$ is upper semicontinuous on $\Delta(0,\rho)$.

Published on 13 Apr 2026 - 23:21

1.7k

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Is there a way to measure how (non)convex a function is, maybe analogous to condition number?

Published on 13 Apr 2026 - 9:52

203

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Corollary 2.1 in Ekeland and Temam on lower semicontinuity

Published on 16 Apr 2026 - 4:54

9.5k

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Optimization with box constraints - via nonlinear function

Published on 10 Apr 2026 - 17:23

281

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Properties on proximal term

Published on 09 Apr 2026 - 11:18

145

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Easy interpretation of matrix multiplication with a set

Published on 12 Apr 2026 - 17:31

822

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convexity of a multivariable function

Published on 11 Apr 2026 - 3:36

137

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Interior of a solid self dual cone

Published on 11 Apr 2026 - 4:23

113

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Measure induced by subgradient of convex functional

Published on 11 Apr 2026 - 3:22

301

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Convexity of the composite of convex function by exponential function

Published on 11 Apr 2026 - 23:43

624

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Why are generalized inequalities defined over proper cone?

Published on 11 Apr 2026 - 8:22

List Question

show the quadratic function $W(x_1,x_2,\ldots,x_n)=A\sum_{i} x_i^2+ \sum_{i\neq j} x_ix_j$ is quasi-concave

Proof: A function is convex iff it is convex when restricted to any line ..

Concave optimization on closed unit ball, using penalty function

Dual polyhedron & dual cone

Prove that $u$ is upper semicontinuous on $\Delta(0,\rho)$.

Is there a way to measure how (non)convex a function is, maybe analogous to condition number?

Corollary 2.1 in Ekeland and Temam on lower semicontinuity

Optimization with box constraints - via nonlinear function

Properties on proximal term

Easy interpretation of matrix multiplication with a set

convexity of a multivariable function

Interior of a solid self dual cone

Measure induced by subgradient of convex functional

Convexity of the composite of convex function by exponential function

Why are generalized inequalities defined over proper cone?

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