unconstrained problem造句

• For unconstrained problems with twice-differentiable functions, some locally Lipschitz functions.
• Constrained problems can often be transformed into unconstrained problems with the help of Lagrange multipliers.
• The Hessian only applies for unconstrained problems.
• Solutions of the successive unconstrained problems will eventually converge to the solution of the original constrained problem.
• I think that the people working in the field have found that the unconstrained problem is harder to solve in practice than the original constrained problem.
• A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem.
• Solving the unconstrained problem is equivalent to finding a point on the convex hull of the family of solutions to an equivalent constrained formulation of the problem.
• Even if the problem has only equality constraints so that the method of Lagrange multipliers yields an unconstrained problem, we do not have a good method for solving unconstrained nonlinear problems.
• If the constrained problem has only equality constraints, the method of Lagrange multipliers can be used to convert it into an unconstrained problem whose number of variables is the original number of variables plus the original number of equality constraints.
• The unconstrained problems are formed by adding a term, called a "'penalty function "', to the objective function that consists of a " penalty parameter " multiplied by a measure of violation of the constraints.
• In each iteration " k " of the method, we increase the penalty coefficient \ sigma _ k ( e . g . by a factor of 10 ), solve the unconstrained problem and use the solution as the initial guess for the next iteration.
• Alternatively, if the constraints are all equality constraints and are all linear, they can be solved for some of the variables in terms of the others, and the former can be substituted out of the objective function, leaving an unconstrained problem in a smaller number of variables.
• Often the solution to these problems can be equivalently ( or approximately ) expressed and solved by converting the formulation to the unconstrained problem \ min \ left \ { D + \ lambda \ cdot R \ right \ } where the Lagrange multiplier \ lambda is a non-negative constant that establishes the appropriate balance between rate and distortion.