Algorithms for nonlinear programming and multiple-objective decisions
Algorithms are solution methods used for optimal decision making in mathematics and operations research. This book is a study of algorithms for decision making with multiple objectives. It is a distillation of recent research in developing methodologies for solving optimal decision problems in economics, and engineering and reflects current research in these areas.
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Optimization of a Single Objective
QUADRATIC PROGRAMMING ALGORITHMS
MultipleObjective Optimization 1Interactive Search
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active constraints Algorithm 2.1 assumptions columns computed consider constrained optimization convergence of xk convergence rate convex convex set decision maker decision problem denote descent direction desired values diagonal element ensure equality constraints equality-constrained equations equivalence establish evaluated formulation given go to Step Hence Hessian inequality constraints interior point interior point methods ipk(xk iteration Jacobian Lagrangian Lemma linear programming linearly independent Math mean-variance method min-max minimization multipliers nonlinear programming null space objective function optimal solution optimization problem orthogonal penalty function penalty parameter portfolio positive-definite positive-semidefinite projected Hessian Proof Q-superlinear convergence quadratic objective function quadratic programming quadratic subproblem quasi-Newton quasi-Newton methods result Rustem satisfied scalar second-order sequence xk sequential quadratic programming shadow prices solving SQP algorithm stepsize strategy stochastic Tapia Theorem 3.1 two-step Q-superlinear unit stepsizes update vector weighting matrix Xk+i yields