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We consider stochastic optimization problems with non-convex functional constraints, such as those arising in trajectory generation, sparse approximation, and robust classification. To this end, we put forth a recursive momentum-based…

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…

This paper proposes a novel nonlinear programming model to capture the equilibrium state of complex supply chain networks. The model, equivalent to a variational inequality model, relaxes traditional strict assumptions to accommodate…

In communication networks, optimization is essential in enhancing performance metrics, e.g., network utility. These optimization problems often involve sum-of-products (or ratios) terms, which are typically non-convex and NP-hard, posing…

Numerical simulations of models and theories that describe complex systems such as spin glasses are becoming increasingly important. Beyond fundamental research, these computational methods also find practical applications in fields like…

Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific…

Designing high-performance error-correcting codes at short blocklengths is critical for low-latency communication systems, where decoding is governed by finite-length and graph-structural effects rather than asymptotic properties. This…

We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…

This paper presents an investigation of two search techniques, tabu search (TS) and simulated annealing (SA), to assess their relative merits when applied to engineering design optimisation. Design optimisation problems are generally…

Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought…

We propose a new method for solving binary optimization problems under inequality constraints using a quantum annealer. To deal with inequality constraints, we often use slack variables, as in previous approaches. When we use slack…

Search-based software engineering (SBSE) addresses critical optimization challenges in software engineering, including the next release problem (NRP) and feature selection problem (FSP). While traditional heuristic approaches and integer…

The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

Alternating minimization heuristics seek to solve a (difficult) global optimization task through iteratively solving a sequence of (much easier) local optimization tasks on different parts (or blocks) of the input parameters. While popular…

Sample average approximation (SAA) is a tractable approach for dealing with chance constrained programming, a challenging stochastic optimization problem. The constraint of SAA is characterized by the $0/1$ loss function which results in…

Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…

Constrained optimization underlies crucial societal problems (for instance, stock trading and bandwidth allocation), but is often computationally hard (complexity grows exponentially with problem size). The big-data era urgently demands…

The alignment of biological networks has the potential to teach us as much about biology and disease as has sequence alignment. Sequence alignment can be optimally solved in polynomial time. In contrast, network alignment is $NP$-hard,…

In this pedagogical work we reviewed the mathematical formalism and the physical interpretation, based on statistical mechanics, of the meta-heuristics called simulated annealing. Moreover, we presented the mathematical formulation of the…