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blegat committed Dec 7, 2023
1 parent 87e82f4 commit 94bc7bc
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2 changes: 1 addition & 1 deletion docs/src/tutorials/Polynomial Optimization/bilinear.jl
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# ## Introduction

# Consider the polynomial optimization problem from [Floudas1999, Section 3.1](@cite).
# Consider the polynomial optimization problem from [Floudas1999; Section 3.1](@cite).

using Test #src
using DynamicPolynomials
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2 changes: 1 addition & 1 deletion docs/src/tutorials/Polynomial Optimization/ellipsoid.jl
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# ## Introduction

# Consider the polynomial optimization problem from [Floudas1999, Section 3.5](@cite)
# Consider the polynomial optimization problem from [Floudas1999; Section 3.5](@cite)

A = [
0 0 1
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# The moment matrix is as follows, we can already see the global minimizer
# `[0, -1]` from the entries `(2, 1)` and `(3, 1)`.
# This heuristic way to obtain solutions to the polynomial optimization problem
# is suggested in [Laurent2008, (6.15)](@cite).
# is suggested in [Laurent2008; (6.15)](@cite).

ν = moment_matrix(con_ref)

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# ## Introduction

# Consider the polynomial optimization problem from [Floudas1999, Section 4.10](@cite)
# Consider the polynomial optimization problem from [Floudas1999; Section 4.10](@cite)
# of minimizing the linear function $-x_1 - x_2$
# over the basic semialgebraic set defined by the inequalities
# $x_2 \le 2x_1^4 - 8x_1^3 + 8x_1^2 + 2$,
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2 changes: 1 addition & 1 deletion docs/src/tutorials/Polynomial Optimization/qp.jl
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# ## Introduction

# Consider the nonconvex Quadratic Program (QP) from [Floudas1999, Section 2.2](@cite)
# Consider the nonconvex Quadratic Program (QP) from [Floudas1999; Section 2.2](@cite)
# that minimizes the *concave* function $c^\top x - x^\top Qx / 2$
# over the polyhedron obtained by intersecting the hypercube $[0, 1]^5$
# with the halfspace $10x_1 + 12x_2 + 11x_3 + 7x_4 + 4x_5 \le 40$.
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