Nonlinear Programming Theory and MethodsSets and functions. The nonlinear programming problem. (Quasi) convexity of functions and related concepts. Feasible sets. Minima; Lagrangian saddle points. Differentiable functions: pseudoconvexity. Ktl-stationary points, duality. Appendix: convexity properties of quadratic functions. The linear simplex method: a reminder. Adjacent vertex methods. Full description methods. Ktl-simplicial methods for quadratic programs. Gradient methods. Cutting plane methods. |
Contents
PART ONE THEORY | 13 |
THE NONLINEAR PROGRAMMING PROBLEM | 36 |
QUASICONVEXITY OF FUNCTIONS AND RELATED | 44 |
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admissible basis algorithm applied basic variables basis entry criterion Br+1 chapter column complementary components concave constraint qualification convex functions convex set corollary corresponding defined denoted differentiable duality eigenvalue eigenvector equality constraints explicitly quasiconvex feasible set finite number G₁ global minimum point go to Step halfspace Hence holds implies inequality infinite edges KTL conditions Lagrangian linear constraints linear programming lower semicontinuous m-vector function Martos matrix MPSubD NLP problem nonempty nonlinear programming nonnegative objective function optimum solution p(x¹ p(x² parametric partial derivatives POINT OPTIMALITY THEOREM polyhedron polytope primal problem programming problem Proof pseudoconvex pseudomonotonic quadratic function quadratic programming quasiconvex functions quasimonotonic r-th iteration saddle point satisfies the basis scalar function sequence simplex tableau solving stationary point tion v'Cv vector changes vertex vertices y(x¹ y(x²