Linear and Nonlinear Programming

<STRONG>1.</STRONG> Introduction. <BR><STRONG>Part I: Linear Programming.</STRONG> <STRONG>2.</STRONG> Basic Properties of Linear Programs.<STRONG>3.</STRONG> The Simplex Method. <STRONG>4.</STRONG> Duality. <STRONG>5.</STRONG> Transportation and Network Flow Problems. <BR><STRONG>Part II: Unconstrained Problems.</STRONG> <STRONG>6.</STRONG> Basic Properties of Solutions and Algorithms. <STRONG>7.</STRONG> Basic Descent Methods. <STRONG>8.</STRONG> Conjugate Direction Methods. <STRONG>9.</STRONG> Quasi- Newton Methods. <BR><STRONG>Part III:</STRONG> <STRONG>Constrained Minimization.</STRONG> <STRONG>10.</STRONG> Constrained Minimization Conditions. <STRONG>11.</STRONG> Primal Methods. <STRONG>12.</STRONG> Penalty and Barrier Methods. <STRONG>13.</STRONG> Dual and Cutting Plane Methods. <STRONG>14.</STRONG> Lagrange Methods. <BR><STRONG>Appendix A:</STRONG> Mathematical Review. <STRONG>A.1.</STRONG> Sets. <STRONG>A.2.</STRONG> Matrix Notation. <STRONG>A.3.</STRONG> Spaces. <STRONG>A.4.</STRONG> Eigenvalues and Quadratic Forms. <STRONG>A.5.</STRONG> Topological Concepts. <STRONG>A.6.</STRONG> Functions. <BR><STRONG>Appendix</STRONG> <STRONG>B:</STRONG> Convex Sets. <STRONG>B.1.</STRONG> Basic Definitions. <STRONG>B.2.</STRONG> Hyperplanes and Polytopes. <STRONG>B.3.</STRONG> Separating and Supporting Hyperplanes. <STRONG>B.4.</STRONG> Extreme Points. <BR><STRONG>Appendix C:</STRONG> Gaussian Elimination. <BR>Bibliography. Index.