To increase the science return of future missions toMars and to enable sample return missions, the accuracy with which a lander can be delivered to the Martian surface must be improved by orders of magnitude. The prior work developed a convex-optimization-based minimum-fuel powered-descent guidance algorithm. In this paper, this convex-optimization-based approach is extended to handle the casew...

We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This allows, in particular, the finding of global minimizers via standard convex minimization schemes.

Bilevel optimization problems with multivalued objective functions in both levels are first replaced by a problem with a parametric lower level using a convex combination of the lower level objectives. Thus a nonconvex multiobjective bilevel optimization problem arises which is then transformed into a parametric bilevel programming problem. The investigated problem has been considered in the pa...

In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global or local op...

Communication delays and synchronization are major bottlenecks for parallel computing, tolerating asynchrony is therefore crucial accelerating computation. Motivated by optimization problems that do not satisfy convexity assumptions, we present an asynchronous block coordinate descent algorithm nonconvex whose objective functions the Polyak-Łojasiewicz condition. This condition a generalization...

This paper presents a brief review and some new developments on the canonical duality theory with applications to a class of variational problems in nonconvex mechanics and global optimization. These nonconvex problems are directly related to a large class of semi-linear partial differential equations in mathematical physics including phase transitions, post-buckling of large deformed beam mode...

We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the direct adaptation of the method to minimize the sum of a proper closed funct...