相关论文: On quadratic optimization problems and canonical d…

We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…

This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…

In recent years, considerable work has been done to tackle the issue of designing control laws based on observations to allow unknown dynamical systems to perform pre-specified tasks. At least as important for autonomy, however, is the…

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

A recent paper by Jordan et al. introduced Decoded Quantum Interferometry (DQI), a novel quantum algorithm that uses the quantum Fourier transform to reduce linear optimization problems -- max-XORSAT and max-LINSAT -- to decoding problems.…

Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…

Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to…

In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…

We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…

Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…

A powerful strategy to treat quantum field theories beyond perturbation theory is by putting them on a lattice. However, the dynamical and symmetry structure of general relativity have for a long time stood in the way of a well-defined…

The paper describes a novel technique that allows to reduce by half the number of delta values that were required to be computed with complexity O(N) in most of the heuristics for the quadratic assignment problem. Using the correlation…

The formalism of causal dynamical triangulations (CDT) provides us with a non-perturbatively defined model of quantum gravity, where the sum over histories includes only causal space-time histories. Path integrals of CDT and their continuum…

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but…

Understanding the continuum limit of a theory of discrete random geometries is a beautiful but difficult challenge. In this optic, we review here the insights that can be obtained for Causal Dynamical Triangulations (CDT) by employing the…

This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…

The paper introduces several new concepts for solving nonconvex or nonsmooth optimization problems, including convertible nonconvex function, exact convertible nonconvex function and differentiable convertible nonconvex function. It is…

Utilizing counterdiabatic (CD) driving - aiming at suppression of diabatic transition - in digitized adiabatic evolution have garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a…