Polynomial Optimization: Theory and Applications

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Related lectures (29)

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Polynomial Optimization: SOS and Nonnegative Polynomials

Explores polynomial optimization, emphasizing SOS and nonnegative polynomials, including the representation of polynomials as quadratic functions of monomials.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Algebraic Geometry: Forms and Maps

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.