This papers presents a convex approximation method for the solution of nonconvex optimal control problems involving input-affine dynamic models. The method relies in the availability of full reference state trajectories. By using these states references as real states trajectories, the dynamic model is approximated such that the resulting problem becomes convex. The convexified problem is solve...

Acceleration–force setups for multi-rigid-body dynamics are known to be inconsistent for some configurations and sufficiently large friction coefficients (a Painleve paradox). This difficulty is circumvented by time-stepping methods using impulse-velocity approaches, which solve complementarity problems with possibly nonconvex solution sets. We show that very simple configurations involving two...

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...

Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamentally difficulties for traditional optimization theory and methods. This paper present...

We consider the problem of locating a user’s position from a set of noisy pseudoranges to a group of satellites. We consider both the nonlinear least squares formulation of the problem, which is nonconvex and nonsmooth, and the nonlinear squared least squares variant, in which the objective function is smooth, but still nonconvex. We show that the squared least squares problem can be reformulat...

In this paper, the multiple-input multiple-output (MIMO) transmit beampattern matching problem is considered. The problem is formulated to approximate a desired transmit beampattern (i.e., an energy distribution in space and frequency) and to minimize the cross-correlation of signals reflected back to the array by considering different practical waveform constraints at the same time. Due to the...

(ABSTRACT) Despite recent advances in convex optimization techniques, the areas of discrete and continuous nonconvex optimization remain formidable, particularly when globally optimal solutions are desired. Most solution techniques, such as branch-and-bound, are enumerative in nature, and the rate of their convergence is strongly dependent on the accuracy of the bounds provided, and therefore, ...

This paper concerns the problem of recovering an unknown but structured signal x ∈ Rn from m quadratic measurements of the form yr = ∣⟨ar,x⟩∣ for r = 1,2, . . . ,m. We focus on the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal (m << n). We formulate the recovery problem as a nonconvex optimization problem where prior structur...

Using some recent results from nonsmooth analysis, we prove the convergence of a new iterative scheme to a solution of a nonconvex equilibrium problem.