Is the following function convex or concave?: {eq}y=x^2 {/eq}Lesson Summary Register to view this lesson Are you a student or a teacher? I am a student I am a teacher Recommended Lessons and Courses for You Rel
Quadratic-exponential functionNonlinear algebraic equationTrialityThis paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-...
2.1 Basic lifting strategies and their core ingredients A QCQP consists of minimizing a quadratic function subject to quadratic constraints, formally given by (1)infx∈K{xTQ0x+2q0Tx−ω0:xTQix+2qiTx≤ωi,i∈[1:m]} where {Qi:i∈[0:m]}⊂Sn, {qi:i∈[1:m]}⊂Rn and ωi are...
Example 21.1 1. The function f(x)=x2 is strongly convex (and, hence, convex and strictly convex) with l = 2. 2. The functions f(x)=x4 and f(x)=ex are strictly convex (and, hence, convex, but not strongly convex). The next two lemmas will be used hereinafter. View chapter ...
ff is convex if and only if ∇2f(x)⪰0 for all x∈dom f∇2f(x)⪰0 for all x∈dom f if ∇2f(x)≻0 ∇2f(x)≻0 for all x∈dom fx∈dom f, then ff is strictly convex examples quadratic function: f(x)=(1/2)xTPx+qTx+rf(x)=(1/2)xTPx+qTx+r (with P∈...
This paper expands the multiparametric quadratic programming (mp-QP) framework presented in Narciso et al. (Comput Chem Eng 164:107882, 2022. https://doi.o
Convex Derivative Quadratic Replies: 3 Forum: Linear and Abstract Algebra J How Does One Compute the Derivative of a Convex Quadratic Function? \frac{d}{dx}f(x)=\frac{d}{dx}[ \frac{1}{2}x_{}^{T}Qx-b_{}^{T}x] how to get this derivative, what is the answer? is there tex...
The feedback law in general is a non-linear function of both time and state, given by the solution of a non-linear partial differential equation. This equation reduces to the well-known Riccati equation if the cost functional is quadratic.M. VIDYASAGAR & S. MUELLER...
Probability density functionUniform/Simpson distributionIn this paper, some integral inequalities for uniformly convex functions are studied by using unordered submajorization for cumulative functions. Strongly convex functions and superquadratic...doi:10.1007/s00010-019-00675-4...
This set is said to be strictly convex if the open segment ]x, y[is contained in A∘ whenever x, y are in A and x≠ y. Let A be a convex subset of E. A function f:E→ℝ¯ is said to be convex (resp. strictly convex) if, given two points x, y in E such that x...