"We get a new multiplicity result for gradient systems. Here is very particular corollary: Let $\Omega\subset {\bf R}^n$ ($n\geq 2$) be smooth bounded domain and let $\Phi:{\bf R}^2\to R}$ $C^1$ function, with $\Phi(0,0)=0$, such that $$\sup_{(u,v)\in R}^2}\frac{|\Phi_u(u,v)|+|\Phi_v(u,v)|}{1+|u|^p+|v|^p}<+\infty$$ where $p>0$, $p=\frac{2}{n-2}$ when $n>2$.\\ Then, every convex set $S\...

A function on R with multiple local minima is approximated from below, via linear programming, by a linear combination of convex kernel functions using sample points from the given function. The resulting convex kernel underestimator is then minimized, using either a linear equation solver for a linear-quadratic kernel or by a Newton method for a Gaussian kernel, to obtain an approximation to a...

We demonstrate the efficiency of the multidomain sampler (MDS) in finding multiple distinct global minima and low-energy local minima in the hydrophobic-polar (HP) lattice protein model. Extending the idea of partitioning energy space in the Wang-Landau algorithm, our approach introduces an additional partitioning scheme to divide the protein conformation space into local basins of attraction. ...

Given a function on Rn with many multiple local minima we approximate it from below, via concave minimization, with a piecewise-linear convex function by using sample points from the given function. The piecewise-linear function is then minimized using a single linear program to obtain an approximation to the global minimum of the original function. Successive shrinking of the original search r...

Search for the global minimum in a molecular energy landscape populated with numerous local minima is a difficult task. Search techniques relevant to such complex spaces can be classified as either global or local. Global search explores the entire space, guaranteeing the global extremum will be found. To accomplish this, the number of samples required grows exponentially with the number of dim...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 27 December 2019Accepted: 10 February 2021Published online: 13 May 2021Keywordsoptimization, landscape, manifold, eigenvalues the Hessian, overparameterizationAMS Subject Headings68T99, 51M99Publication DataISSN (online): 2577-0187Publisher: Society for Industrial and App...