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1. Convex Programming Prove that the following mathematical program is a convex program. You may use without proof any facts claimed about convex functions and sets in the lecture slides. min max(1/1, 1/₂) 1,2 I1, I2 > 0 x² + x² ≤ 1

1. Convex Programming Prove that the following mathematical program is a convex program. You may use without proof any facts claimed about convex functions and sets in the lecture slides. min max(1/1, 1/₂) 1,2 I1, I2 > 0 x² + x² ≤ 1

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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1. Convex Programming Prove that the following mathematical program is a convex program. You may use without proof any facts claimed about convex functions and sets in the lecture slides. min max(1/₁, 1/₂) 1,2 F1, F₂ > 0 x² + x² ≤ 1 2. Propositional Inference Suppose you want to show: A^B^ (B⇒D) ^ ((A^D) E) ^ ((BAC) ⇒F) ^ (A⇒C) ^ (F⇒G) G (a) Draw the diagram we used in the video for forward and backward chaining. (b) Indicate the order in which symbols are popped from the agenda by forward chaining (c) Indicate the order in which subgoals are added to the stack by backwards chaining (d) Prove the entailment using resolution. (You do not need to show every clause generated, just those on the path to G. (e) Draw the tree of models explored by DPLL to prove the entailment. 3. Limits of Forward Chaining Given an example of an entailment that can be inferred via resolution but cannot be inferred using forward chaining
Transcribed Image Text:1. Convex Programming Prove that the following mathematical program is a convex program. You may use without proof any facts claimed about convex functions and sets in the lecture slides. min max(1/₁, 1/₂) 1,2 F1, F₂ > 0 x² + x² ≤ 1 2. Propositional Inference Suppose you want to show: A^B^ (B⇒D) ^ ((A^D) E) ^ ((BAC) ⇒F) ^ (A⇒C) ^ (F⇒G) G (a) Draw the diagram we used in the video for forward and backward chaining. (b) Indicate the order in which symbols are popped from the agenda by forward chaining (c) Indicate the order in which subgoals are added to the stack by backwards chaining (d) Prove the entailment using resolution. (You do not need to show every clause generated, just those on the path to G. (e) Draw the tree of models explored by DPLL to prove the entailment. 3. Limits of Forward Chaining Given an example of an entailment that can be inferred via resolution but cannot be inferred using forward chaining
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