Java利用单纯形法实现线性规划的值求解（最优值，无界，无可行解），适用于，max cx，subject to Ax = b,x≥0。min cx，subject to Ax = b,x≥0。min c′Ty A′y = b′,B′y≥0,类似线性规划问题。标准形式可用，一般形式也可以用。

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线性规划单纯形法求取最优解，有程序说明，已：min 3x1+2x2+x3-x3 s．t． x1-2x2+3x3-x4≤15 2x1+x2-x3+2x4≤10 x1，x2，x3，x4≥0 题目为例

LECTURE 6: CONVERGENCE OF AN ALGORITHM 1. Concept of convergence 2. Rate of convergence LECTURE 7: CONSTRAINED OPTIMIZATION - INTRODUCTION 1. Basic terminologies 2. KKT conditions – motivation 3. Background knowledge LECTURE 8: CONSTRAINED OPTIMIZATION – OPTIMALITY CONDITIONS 1. Basic concepts 2. Necessary conditions – KKT conditions 3. Sufficient conditions LECTURE 9: CONSTRAINED OPTIMIZATION – SENSITIVITY ANALYSIS AND DUALITY 1. Basic concepts 2. Sensitivity analysis 3. Duality theory LECTURE 10: CONSTRAINED OPTIMIZATION – LAGRANGIAN DUAL PROBLEM 1. Lagrangian dual problem 2. Duality gap 3. Saddle point solution LECTURE 11: SOLUTION METHODS FOR CONSTRAINED OPTIMIZATION 1. Primal approach 2. Penalty and barrier methods 3. Dual approach 4. Primal-dual approach LECTURE 12: QUADRATICALLY CONSTRAINED QUADRATIC PROGRAMMING (QCQP) 1. Motivation 2. Convex QCQP 3. General QCQP 4. On-Going Research

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