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Question on equivalent definitions of a convex function

Published on
#real-analysis #convex-analysis
54
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How can I find the dual problem to the following convex problem?

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#convex-analysis #convex-optimization #lagrange-multiplier #duality-theorems
63
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How to proceed in finding the conjugate of the following?

Published on
#convex-analysis #convex-optimization
74
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Solution's existence condition of an under-determined linear system with linear constraints

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#linear-algebra #inequality #convex-analysis #linear-programming
2k
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Hyperplane and associated Half spaces convexity

Published on
#convex-analysis
903
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Using Fenchel-Rockafellar duality to obtain linear programming duality

Published on
#convex-analysis #convex-optimization #duality-theorems
57
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Interpreting nonnegativity of inner product in multiple dimensions

Published on
#real-analysis #convex-analysis #convex-geometry
307
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Convex combination of $2^n$ vectors from cartesian products of half-spaces

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#combinatorics #convex-analysis #convex-geometry #convex-hulls
2.7k
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Proof of the convexity of the unit circle using the distance between two points

Published on
#convex-analysis #normed-spaces #circles
194
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Convexify this optimization problem with one nonlinear (bilinear) constraint

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#convex-analysis #convex-optimization #nonlinear-optimization #constraints
165
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How is this constraint convex?

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#convex-analysis #convex-optimization
1.7k
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Dual ascent and gradient of convex conjugate

Published on
#optimization #convex-analysis #convex-optimization
44
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Strict dominance wrt distances to vertices in a convex hull

Published on
#geometry #convex-analysis #analytic-geometry
670
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Letting $x_n\to x$ weakly in a normed vector space $X$, prove the following statement.

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#general-topology #functional-analysis #operator-theory #convex-analysis #weak-convergence
74
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Union of interiors of convex sets

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#general-topology #convex-analysis

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