Optimization Techniques
24EST372 · S3 · 4 credits
Official KTU 2024 syllabus subject — study with practice, PYQs and AI tools.
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Module 01Unconstrained problemsexpand
maxima and minima- global maxima and minima-local maxima and minima- inflection and saddle points. Necessary and sufficient conditions- A necessary condition for a stationary point to be an extreme point, A sufficient condition for a stationary point to be an extremum using Hessian matrix.
Module 02Solution of Simultaneous Nonlinear Equationsexpand
General form of simultaneous nonlinear equation-solution-Algorithm for solving simultaneous nonlinear equations -Newton Raphson method.
Module 03Optimization of Equality Constrained Continuous Functionsexpand
Constrained continuous functions, constrained problems, Equality constraints, Constrained derivatives (Jacobian) method- Jacobian matrix and control matrix, Lagrangean method- Lagrange multipliers.
Module 04Optimization of Inequality Constrained Continuous Functionsexpand
Constrained problems, Inequality constraints, Lagrangean method to problems with inequality constraints, Karush–Kuhn–Tucker (KKT) necessary conditions for determining the stationary points.
Module 05Unconstrained Algorithmsexpand
Unimodal single-variable functions, interval of uncertainty, Direct search methods-dichotomous and golden section. Twice continuously differentiable functions, Gradient method (steepest ascent method).
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