A SQP Method for Inequality Constrained Optimization

Abstract In this paper, a new SQP method for inequality constrained optimization is proposed and the globalconvergence is obtained under very mild conditions.     

Concave Programming in Control Theory

We show in the present paper that many open and challenging problems in control theory belong the the class of concave minimization programs. More precisely, these problems can be recast as the minimization of a concave objective function over convex LMI (Linear Matrix Inequality) constraints. As concave programming is the best studied class of problems in global optimization, several concave programs such as simplicial and conical partitioning algorithms can be used for the resolution. Moreover, these global techniques can be combined with a local Frank and Wolfe feasible direction algorithm and improved by the use of specialized stopping criteria, hence reducing the overall computational overhead. In this respect, the proposed hybrid optimization scheme can be considered as a new line of attack for solving hard control problems.Computational experiments indicate the viability of our algorithms, and that in the worst case they require the solution of a few LMI programs. Power and efficiency of the algorithms are demonstrated for a realistic inverted-pendulum control problem.Overall, this dedication reflects the key role that concavity and LMIs play in difficult control problems.     

Solving a Class of Multiplicative Programs with 0–1 Knapsack Constraints

We develop a branch-and-bound algorithm to solve a nonlinear class of 0–1 knapsack problems. The objective function is a product of m2 affine functions, whose variables are mutually exclusive. The branching procedure in the proposed algorithm is the usual one, but the bounding procedure exploits the special structure of the problem and is implemented through two stages: the first stage is based on linear programming relaxation; the second stage is based on Lagrangian relaxation. Computational results indicate that the algorithm is promising.     

Generalized γ-Valid Cut Procedure for Concave Minimization

The concept of a -valid cutting plane has been used in many types of algorithms for solving concave minimization problems. Unfortunately, the procedures proposed to date for constructing these cuts are valid only under certain assumptions that often may not hold in practice. Chief among these is the requirement that the feasible region of the concave minimization problem in question have full dimension, and that the objective function of this problem be concave rather than quasiconcave. In this article, we propose, validate, and show how to implement a more general -valid cutting plane procedure which eliminates these restrictions.     

关于双层规划约束规格的一个注记

本文表明了非线性规划中常见的约束规格对一般双层规划不成立,并对双层规划可以满足的较弱的约束规格“部分平静”,给出了使其成立的充分条件．     

A variable-metric method for function minimization derived from invariancy to nonlinear scaling

The effect of nonlinearly scaling the objective function on the variable-metric method is investigated, and Broyden's update is modified so that a property of invariancy to the scaling is satisfied. A new three-parameter class of updates is generated, and criteria for an optimal choice of the parameters are given. Numerical experiments compare the performance of a number of algorithms of the resulting class.The author is indebted to Professor S. S. Oren, Economic Engineering Department, Stanford University, Stanford, California, for stimulating discussions during the development of this paper. He also recognizes the financial support by the National Research Council of Italy (CNR) for his stay at Stanford University.     

Editorial policy

This note uses the closure error function of Freudenstein's equation for a four-bar linkage to determine the initial dimensions of the links of a path-generating mechanism. The sum of the absolute values of the errors of the output angles is then taken as the cost function for optimization. Successive one-dimensional optimization in the coordinate directions is then used for the design of four-bar function generators. This method is simpler than other methods, and the work of calculation is less than for other methods.Many discussions with Associate Professor F. Y. Li, Department of Mechanical Engineering, Tianjin College of Light Industry, are gratefully acknowledged.     

A Simple Primal-Dual Feasible Interior-Point Method for Nonlinear Programming with Monotone Descent

We propose and analyze a primal-dual interior point method of the feasible type, with the additional property that the objective function decreases at each iteration. A distinctive feature of the method is the use of different barrier parameter values for each constraint, with the purpose of better steering the constructed sequence away from non-KKT stationary points. Assets of the proposed scheme include relative simplicity of the algorithm and of the convergence analysis, strong global and local convergence properties, and good performance in preliminary tests. In addition, the initial point is allowed to lie on the boundary of the feasible set.     

Variational Principles, Minimization Theorems, and Fixed-Point Theorems on Generalized Metric Spaces

In this paper, we prove a new minimization theorem by using the generalized Ekeland variational principle. We apply our minimization theorem to obtain some fixed-point theorems. Our results extend, improve, and unify many known results due to Kui, Ekeland, Takahashi, Caristi, iri, and others.