For a function on RR, quasiconvexity requires that each sublevel set to be an interval. All convex functions are quasiconvex, but not all quasiconvex functions are convex, so quasiconvexity is a generaliza
4.1.3 定义(凹函数)concave function 空间\mathbb{R}^n 上的子集S 上的函数f 是凹函数,当它的相反函数-f 是凸函数时,这个函数在子集S 上就是凹函数。 也即是,在空间\mathbb{R}^{n+1} 中的子集epi(-f) 是一个凸集时,函数f 就是空间\mathbb{R}^n 中的子集S 上的凹函数。
Hessian equationsSupport functionMinkowski additionWe study the class Q of quasiconvex functions (i.e. functions with convex sublevel sets), by associating to every u is an element of Q boolean AND C(R-n) a function H:R-n x R -> R boolean OR {+/-infinity}, such that H(X, t) ...
On Discrete Hessian Matrix and Convex ExtensibilityTheoretical or Mathematical/ Hessian matricesmathematical programming/ discrete Hessian matrixconvex extensibilityinteger lattice pointsL-convex functionM-convex functiondiscrete functionsdiscrete convex analysis...
where hK is the support function of K (see Sect. 2.1 for the definition) and the Hessian matrix of hK. Here, we write [A]j for the jth elementary symmetric function of the eigenvalues of a symmetric matrix A and use the convention that [A]0=1. We write for (n−1)-dimensional ...
M11M11is200200(we removed line 1 and column 1). M22M22is1200x2−400y+21200x2−400y+2(we removed line 2 and column 2). If the function is convex, these minors should be nonnegativeon the interior of the convex set. Which convex set? By definition, the domain of a convex functi...
(iii). Strict convexity: a function f is strictly convex if and only if ∇2f is positive definite in domf . (iv). Strict concavity: a function f is strictly concave if and only if ∇2f is negative definite in domf . Where ∇2f is the Hessian matrix of f which is defined at...
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Definition B.2 Let A be a strongly convex subset of a complete Riemannian manifold M, and f:A→R. Then, f is called convex (respectively, strictly convex) if f(γx,y(t)) is a convex (respectively, strictly convex) function of the time parameter t, for all x, y∈ A. Further, ...
The full Hessian matrix is checked against a possibly very small negative eigenvalue due to rounding errors. The calling sequence is similar to quadprog except that there is no starting point x0 argument. Option is limited to a tolerance tol and a maximum of iterations. The exitflag convention...