In this paper a new method is introduced for path planning of an autonomous vehicle. In this method, the environment is considered cluttered and with some uncertainty sources. Thus, the state of detected object should be estimated using an optimal filter. To do so, the state distribution is assumed Gaussian. Thus the state vector is estimated by a Kalman filter at each time step. The estimation...

Using a regularized Nikaido-Isoda function, we present a (nonsmooth) constrained optimization reformulation of a class of generalized Nash equilibrium problems (GNEPs). Further we give an unconstrained reformulation of a large subclass of all GNEPs which, in particular, includes the jointly convex GNEPs. Both approaches characterize all solutions of a GNEP as minima of optimization problems. Th...

Abstract In the present paper we propose to rewrite a nonsmooth problem subjected convex constraints as an unconstrained problem. We show that this novel formulation shares same global and local minima with original constrained Moreover, reformulation can be solved standard optimization methods if are able make projections onto feasible sets. Numerical evidence shows proposed compares favorably...

In the paper, we present an algorithm framework for the more general problem of minimizing the sum f(x) + ψ(x), where f is smooth and ψ is convex, but possible nonsmooth. At each step, the search direction of the algorithm is obtained by solving an optimization problem involving a quadratic term with diagonal Hessian and Barzilai-Borwein steplength plus ψ(x). The method with the nomonotone line...

Stochastic composition optimization draws much attention recently and has been successful in many emerging applications of machine learning, statistical analysis, and reinforcement learning. In this paper, we focus on the composition problem with nonsmooth regularization penalty. Previous works either have slow convergence rate, or do not provide complete convergence analysis for the general pr...

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate and variable sample size strategy employed. proposed algorithm combines an SAA subgradient spectral coefficient order provide suitable direction which improves performance first method as shown by numerical results....

We present several state-of-the-art first-order methods for well-structured large-scale nonsmooth convex programs. In contrast to their black-boxoriented prototypes considered in Chapter 5, the methods in question utilize the problem structure in order to convert the original nonsmooth minimization problem into a saddle-point problem with a smooth convex-concave cost function. This reformulatio...

This paper presents, within a unified framework, a potentially powerful canonical dual transformation method and associated generalized duality theory in nonsmooth global optimization. It is shown that by the use of this method, many nonsmooth/nonconvex constrained primal problems in Rn can be reformulated into certain smooth/convex unconstrained dual problems in Rm with m 6 n and without duali...