第 33 / 79 页
非代码面试题
显示 20 / 1576 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
3335Time Needed for a Mode to Shrink by a Factor e^-1For the mode \sin(3x) evolving under u t=2u xx , after what time does its amplitude shrink by a factor of e -1 ?数学中等derivation未尝试面试订阅3336Why High-Frequency Modes Die FirstWhy does the heat equation smooth out small-scale wiggles faster than large-scale structure?数学中等essay未尝试面试订阅3337Maximum Principle IntuitionWhy can the heat equation not spontaneously create a new interior maximum if there is no internal heat source?数学中等essay未尝试面试订阅3338Boundary Conditions MatterWhy do boundary conditions qualitatively matter for heat diffusion on a finite interval?数学中等essay未尝试面试订阅3339Diffusion as Local AveragingExplain in words why the heat equation can be viewed as repeated local averaging.数学中等essay未尝试面试订阅3340Why Diffusion Forgets Fine Initial DetailsWhy does long-time heat evolution remember coarse mass distribution more than fine initial details?数学中等essay未尝试面试订阅3341Projected Optimum Above the FloorMinimize (x-2) 2 subject to x\ge 0. Using the KKT form g(x)=0-x\le 0, find the optimizer x * and the optimal multiplier .数学简单derivation未尝试面试订阅3345Negative Target, Mildly Active FloorMinimize (x--2) 2 subject to x\ge -1. Using the KKT form g(x)=-1-x\le 0, find the optimizer x * and the optimal multiplier .数学简单derivation未尝试面试订阅3346Closest Point to the Origin Above a Budget LineMinimize x 2+y 2 subject to x+y\ge 1. Find (x *,y *) and the optimal KKT multiplier for the inequality g(x,y)=1-x-y\le 0.数学中等derivation未尝试面试订阅3351Weighted Quadratic with Cheap x and Expensive yMinimize 1x 2+3y 2 subject to x+y\ge 4. Find (x *,y *) and the KKT multiplier.数学中等derivation未尝试面试订阅3356Feasible Center Means Zero MultiplierConsider minimizing (x-1) 2+(y-1) 2 subject to x+y\ge 1. At the optimum, is the inequality active or inactive, and what does KKT imply about ?数学中等derivation未尝试面试订阅3358Offset Point Already FeasibleConsider minimizing (x-2) 2+(y--1) 2 subject to x+y\ge 0. At the optimum, is the inequality active or inactive, and what does KKT imply about ?数学中等derivation未尝试面试订阅3360High y Coordinate Makes the Constraint SlackConsider minimizing (x--1) 2+(y-3) 2 subject to x+y\ge 1. At the optimum, is the inequality active or inactive, and what does KKT imply about ?数学中等derivation未尝试面试订阅3361Why Convexity Makes KKT So PowerfulWhy do KKT conditions become sufficient, not just necessary, in many convex optimization problems?数学中等essay未尝试面试订阅3362Complementary Slackness as an Economic StatementExplain complementary slackness in plain language to a PM who thinks of constraints as scarce resources.数学中等essay未尝试面试订阅3363When KKT Is Not Enough by ItselfGive one reason why solving the KKT equations in a nonconvex problem may fail to identify the global optimum.数学中等essay未尝试面试订阅3364Shadow Price InterpretationWhy is the optimal multiplier often interpreted as the marginal value of relaxing or tightening a constraint?数学中等essay未尝试面试订阅3365Why Slater-Type Regularity MattersWhy do regularity conditions such as Slater's condition matter when applying KKT?数学中等essay未尝试面试订阅3368Midpoint Rule Exact on a LineUsing a single-panel midpoint rule, approximate \int 0 4 (1+x)\,dx.数学简单derivation未尝试面试订阅3369Trapezoid Rule on a Symmetric Convex FunctionUsing a single-panel trapezoid rule, approximate \int -1 1 x 2\,dx.数学简单derivation未尝试面试订阅