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We show how the localization landscape, originally introduced to bound low energy eigenstates of disordered wave media and many-body quantum systems, can form the basis for hardware-efficient quantum algorithms for solving binary…
We propose an extended genetic algorithm (GA) with different local environmental conditions. Genetic entities, or configurations, are put on nodes in a ring structure, and location-dependent environmental conditions are applied for each…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
The aging dynamics of a simple model glass is numerically investigated observing how it takes place in the potential energy landscape $V$. Partitioning the landscape in basins of minima of $|\nabla V|^2$, we are able to elucidate some…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
We compute the statistical distribution of index-1 saddles surrounding a given local minimum of the $p$-spin energy landscape, as a function of their distance to the minimum in configuration space and of the energy of the latter. We…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm…
We revisit the concept of marginal stability in glasses, and determine its range of applicability in the context of avalanche-type response to slow external driving. We argue that there is an intimate connection between a pseudo-gap in the…
The chapter starts with a historical summary of first attempts to optimize the spin glass Hamiltonian, comparing it to recent results on searching largest cliques in random graphs. Exact algorithms to find ground states in generic spin…
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
A minimal surface in a random environment (MSRE) is a surface which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary conditions. Apart from their intrinsic interest, such surfaces…
Several standard processes for searching minima of potential functions, such as thermodynamical strategies (simulated annealing) and biologically motivated selfreproduction strategies, are reduced to Schr\"odinger problems. The properties…
We consider the problem of finding nearly optimal solutions of optimization problems with random objective functions. Two concrete problems we consider are (a) optimizing the Hamiltonian of a spherical or Ising $p$-spin glass model, and (b)…
In this work we study spin-glass (SG) like behavior in the dynamics of multiple agents in a social or economic context using interactions which are similar to the physical case. The different preferences shown by individual agents are…
Locating the global minimum of a complex potential energy surface is facilitated by considering a homotopy, namely a family of surfaces that interpolate continuously from an arbitrary initial potential to the system under consideration.…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to…
We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces…