Variational Calculus and Optimal Control: Optimization with Elementary Convexity Book

	Preface
Ch. 0	Review of Optimization in R[superscript d]	1
Ch. 1	Standard Optimization Problems	13
Ch. 2	Linear Spaces and Gateaux Variations	36
Ch. 3	Minimization of Convex Functions	53
Ch. 4	The Lemmas of Lagrange and Du Bois-Reymond	97
Ch. 5	Local Extrema in Normed Linear Spaces	103
Ch. 6	The Euler-Lagrange Equations	145
Ch. 7	Piecewise C[superscript 1] Extremal Functions	197
Ch. 8	Variational Principles in Mechanics	234
Ch. 9	Sufficient Conditions for a Minimum	282
Ch. 10	Control Problems and Sufficiency Considerations	341
Ch. 11	Necessary Conditions for Optimality	378
	App. A.0. Compact Sets in R[superscript d]	419
	App. A.1. The Intermediate and Mean Value Theorems	421
	App. A.2. The Fundamental Theorem of Calculus	423
	App. A.3. Partial Integrals: Leibniz' Formula	425
	App. A.4. An Open Mapping Theorem	427
	App. A.5. Families of Solutions to a System of Differential Equations	429
	App. A.6. The Rayleigh Ratio	435
	App. A.7. Linear Functionals and Tangent Cones in R[superscript d]	441
	Bibliography	445
	Historical References	450
	Answers to Selected Problems	452
	Index	457