calculusoptimizationconcept imageOptimization problems in first semester calculus have historically been a challenge for students. Focusing on the classic optimization problem of finding the minimum amount of fencing required to enclose a fixed area, we examine students'' activity through the lens of ...
Learn what optimization means in calculus. Discover the optimization problems. Learn the steps to solve the optimization problems. See optimization...
MOS-SIAM Series on Optimization(共34册),这套丛书还有 《Variational Analysis in Sobolev and BV Spaces》《Introduction to Optimization and Hadamard Semidifferential Calculus》《Algebraic and Geometric Ideas in the Theory of Discrete Optimization》《A Mathematical View of Interior-point Methods in Convex ...
This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present.\nBeginning with the scientific modeling that motivates the subject, the book then tackles mathematical quest...
and Applications(共19册),这套丛书还有 《Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations》《Nonlinear Spectral Theory》《Optimization in Function Spaces》《Optimization in Function Spaces》《Relaxation in Optimization Theory and Variational Calculus》等。
In the absence of any constraint, our problem reduces to(Ⅰ), this is just standard (albeit multivariate) calculus! So we know that the minimal value of f is an extremum of the function. How can we pick a vector x∗=(x1∗,...,xn∗) so that f reaches a global minimum? From...
In the absence of additional constraints the solution to the unconstrained maximization problem is easy to derive using basic calculus and equals x^=c−1Σ−1α. We would like to understand the difference x∗−x^, where x∗ is the solution of (8.12), and in particular to measure ...
We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that ...
Ch 1. Graphing and Functions Ch 2. Continuity Ch 3. Vectors in Calculus Ch 4. Geometry and Trigonometry Ch 5. How to Use a Scientific... Ch 6. Limits Ch 7. Rate of Change Ch 8. Calculating Derivatives and Derivative... Ch 9. Graphing Derivatives and L'Hopital's... Ch 10. Applic...
In this post, we take a look at a problem that plagues training of neural networks, pathological curvature.