in this book we aim to present， in a unified framework， a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization， equilibrium， control， and stability of linear and nonlinear systems. the title variational analysis refiects this breadth. for a long time， variational problems have been identified mostly with the 'calculus of variations'. in that venerable subject， built around the minimization of integral functionals， constraints were relative

chapter 1. max and min
a. penalties and constraints
b. epigraphs and semicontinuity
c. attainment of a minimum
d. continuity, closure and growth
e. extended arithmetic
f. parametric dependence
g. moreau envelopes
h. epi-addition and epi-multiplication
i*. auxiliary facts and principles
commentary

chapter 2. convexity
a. convex sets and functions
b. level sets and intersections chapter 1. max and min a. penalties and constraints b. epigraphs and semicontinuity c. attainment of a minimum d. continuity, closure and growth e. extended arithmetic f. parametric dependence g. moreau envelopes h. epi-addition and epi-multiplication i*. auxiliary facts and principles commentary chapter 2. convexity a. convex sets and functions b. level sets and intersections c. derivative tests d. convexity in operations e. convex hulls f. closures and contimuty g.* separation h* relative interiors i* piecewise linear functions j* other examples commentary chapter 3. cones and cosmic closure a. direction points b. horizon cones c. horizon functions d. coercivity properties e* cones and orderings f* cosmic convexity g* positive hulls commentary chapter 4. set convergence a. inner and outer limits b. painleve-kuratowski convergence c. pompeiu-hausdorff distance d. cones and convex sets e. compactness properties f. horizon limits g* contimuty of operations h* quantification of convergence i* hyperspace metrics commentary chapter 5. set-valued mappings a. domains, ranges and inverses b. continuity and semicontimuty c. local boundedness d. total continuity e. pointwise and graphical convergence f. equicontinuity of sequences g. continuous and uniform convergence h* metric descriptions of convergence i* operations on mappings j* generic continuity and selections commentary . chapter 6. variational geometry a. tangent cones b. normal cones and clarke regularity c. smooth manifolds and convex sets d. optimality and lagrange multipliers e. proximal normals and polarity f. tangent-normal relations g* recession properties h* irregularity and convexification i* other formulas commentary chapter 7. epigraphical limits a. pointwise convergence b. epi-convergence c. continuous and uniform convergence d. generalized differentiability e. convergence in minimization f. epi-continuity of function-valued mappings g. continuity of operations h* total epi-convergence i* epi-distances j* solution estimates commentary chapter 8. subderivatives and subgradients a. subderivatives of functions b. subgradients of functions c. convexity and optimality d. regular subderivatives e. support functions and subdifferential duality f. calmness g. graphical differentiation of mappings h* proto-differentiability and graphical regularity i* proximal subgradients j* other results commentary chapter 9. lipschitzian properties a. single-valued mappings b. estimates of the lipschitz modulus c. subdifferential characterizations d. derivative mappings and their norms e. lipschitzian concepts for set-valued mappings …… chapter 10. subdifferential calculus chapter 11. dualization chapter 12. monotone mappings chapter 13. second-order theory chapter 14. measurability