finalized chapter, added references and html

Author: Wu

class08/Consensus_for_Optimal_Control.pdf

@@ -41,7 +41,11 @@ References:
 
 * Olfati-Saber, Reza, J. Alex Fax, and Richard M. Murray. "Consensus and cooperation in networked multi-agent systems." Proceedings of the IEEE 95.1 (2007): 215-233.
 
+* Boyd, Stephen, et al. "Distributed optimization and statistical learning via the alternating direction method of multipliers." Foundations and Trends® in Machine learning 3.1 (2011): 1-122.
 
+* Summers, Tyler H., and John Lygeros. "Distributed model predictive consensus via the alternating direction method of multipliers." 2012 50th annual Allerton conference on communication, control, and computing (Allerton). IEEE, 2012.
+
+* Piansky, R., Stinchfield, G., Kody, A., Molzahn, D. K., & Watson, J. P. (2024). Long duration battery sizing, siting, and operation under wildfire risk using progressive hedging. Electric Power Systems Research, 235, 110785.
 """
 
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@@ -209,7 +213,7 @@ Defining the quadratic disagreement function $\varphi(x) = \frac{1}{2} x^T L x$,
 """
 
 # ╔═╡ 46a8121f-f1aa-4d22-8ef9-1d02f957767d
-question_box(md"""What motivates the division by 2 in the quadratic disagreement funcion?""")
+question_box(md"""What motivates the division by 2 in the quadratic disagreement function?""")
 
 # ╔═╡ 85b74a70-a8df-4741-aa1b-d551d0e9bea2
 Foldable(md"Answer...", md"It accounts for the double-counting of undirected edges in the graph.")
@@ -779,7 +783,7 @@ We now consider a __more general form of consensus__, beyond the global consensu
 $\sum_i f_i(x_i)$.
 
 Each local variable $x_i$ contains a subset of components that correspond to certain components of a global variable $z$. We define a mapping $\mathcal{G}(i, j)$ from a local index $(i, j)$ to the corresponding global index $g$, such that
-$(x_i)j = z{\mathcal{G}(i, j)}$.
+$(x_i)_j = z_{\mathcal{G}(i, j)}$.
 
 As a motivating example, consider a __model fitting__ problem. Here, the global variable $z$ represents the full feature vector, while each processor (or node) $i$ holds a subset of the data. The corresponding local variable $x_i$ represents the subset of features in $z$ that appear in block $i$ of the data. This structure is typical in large-scale, high-dimensional datasets that are __sparse__ and __distributed__ across multiple computing nodes.
 
@@ -1143,7 +1147,7 @@ In this chapter, we introduced __consensus__:
 
 * a mechanism for __agreement__ among agents through local communication
 * convergence guaranteed under __connectivity__ and __convexity__
-* enables coordination wtihout centralized control (scalable, robust)
+* enables coordination without centralized control (scalable, robust)
 
 We also introduced __ADMM__, a powerful optimization framework:
 
@@ -1163,20 +1167,20 @@ question_box(md"""Consensus and ADMM rely on cooperation and information exchang
 Foldable(md"Hint...", md"In such _adversarial_ or _strategic_ environments, the assumptions of standard consensus no longer hold. The optimization must be reformulated. It becomes __equilibrium-seeking__ rather than __agreement-seeking__.")
 
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