In this paper we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globall
使用IRIS算法生成convex regions; 整数规划来表示不同regions的选择; 限定多项式曲线在空间多面体中,在多项式阶数为1的情况下是一个MIQP,3的情况下是一个MISOCP,一般情况下是一个MISDP问题; 由于求解稳定性的问题一般情况下考虑阶数为3的情况下,目标函数是一个minimum jerk的问题; 提出一种解法是先使用3阶的情况进行...
We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This leaves only a lower order linear term (in the dimension) a...
9 Mixed integer optimizationIn other chapters of this cookbook we have considered different classes of convex problems with continuous variables. In this chapter we consider a much wider range of non-convex problems by allowing integer variables. This technique is extremely useful in practice, and ...
We extend a result of Dash (International Conference on Integer Programming and Combinatorial Optimization (IPCO), pp. 145–160, 2002) to the nonlinear setting which shows that for convex 0/1 problems, CP does at least as well as BB, with variable disjunctions. We sharpen this by giving ...
We survey mixed-integer programming techniques as they are applied in bilevel optimization. • We focus on bilevel problems with convex or linear lower-level problems as well as on problems with mixed-integer lower levels. • Special attention is given to bilevel pricing problems, Stackelberg...
As first formulated, you try to maximize the objective function. However, all Optimization Toolbox™ solvers minimize. So formulate the problem as minimizing the negative of the objective: minxλxTQx-rTx. This objective function is nonlinear. The MILP solver requires a linear objective function....
"The Cutting-Plane Method for Solving Convex Programs." J. Soc. Indust. Appl. Math. Vol. 8, No. 4, pp. 703-712, December, 1960. MATLAB® Problem Formulation To express optimization problems: Decide what your variables represent Express lower and upper bounds in these variables Give ...
This books presents the fundamentals of nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis in chemical engineering. The reader is acquainted with the basics of convex analysis and nonlinear optimization and is introduced to the elementary concepts ...
A prerequisite for so doing is a convexity theory for dynamic optimization as well as the ability to build valid convex relaxations for Bolza-type functionals. For solving dynamic optimization problems globally, our focus is on the use of branch-and-bound algorithms; on the other hand, MIDO ...