The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed in the paper and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive system. It is shown how the speed dependent constrai...

In this paper, we propose the first exact algorithm for minimizing the difference of two submodular functions (D.S.), i.e., the discrete version of the D.C. programming problem. The developed algorithm is a branch-and-bound-based algorithm which responds to the structure of this problem through the relationship between submodularity and convexity. The D.S. programming problem covers a broad ran...

Fuzzy modelling has interpretability of the obtained models as a fundamental goal. In this paper a control-oriented local-model fuzzy clustering algorithm will try that local models approximate the linearized plant model on their validity zones. A family of clustering algorithms is presented so that it incorporates some desirable characteristics regarding convexity and smoothness of the final i...

Many physical simulators linearize contact constraints such that each contact constraint defines a half-space in the configuration space of the effected objects. By modeling contact constraints as infinitely extending half spaces it is only possible to approximate regions in configuration space that are locally convex. This implicit assumption of local convexity introduces artifacts in the resu...

We present some sufficient conditions ensuring the upper semicontinuity and the continuity of the Bregman projection operator ΠgC and the relative projection operator P g C in terms of the D-approximate (weak) compactness for a nonempty closed set C in a Banach space X. We next present certain sufficient conditions as well as equivalent conditions for the convexity of a Chebyshev subset of a Ba...

The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for the solution of such problems is derived by using logarithm barrier function. In this paper we have made an attempt to solve the linear constrained optimizati...

The extremum properties of the generalized Rayleigh quotient related to flutter instability are investigated. It is shown that, in addition to the well-known stationary property, under certain circumstances the quotient exhibits maximum-minimum properties which are in contrast to those of the classical Rayleigh quotient. One consequence is that an approximate method of stability analysis using ...

In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the -constraint method, the Benson method, the hybrid method and the elastic -constrai...

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on difference of convex (DC) programming, and enjoys both strong computational and statistical guarantees. Specifically, by leveraging a sophisticated characterization of ...

The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in L is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angula...