PDE-constrained optimization is a subset of mathematical optimization where at least one of the constraints may be expressed as a partial differential...

equations (PDE) and performing PDE-constrained optimization. The primary applications are computational fluid dynamics and aerodynamic shape optimization, but...

Youngsoo (2011). "PDE-constrained Optimization and Beyond" (PDF). Heinkenschloss, Matthias (2008). "PDE Constrained Optimization" (PDF). SIAM Conference...

Hydrological optimization applies mathematical optimization techniques (such as dynamic programming, linear programming, integer programming, or quadratic...

application in robotics, traffics, and games, optimization applications in finance, as well as PDE-constrained optimization. Nocedal was born and raised in Mexico...

{\displaystyle g(x)=0~.} The solution corresponding to the original constrained optimization is always a saddle point of the Lagrangian function, which can...

multi-objective optimization problem which requires manually weighing the loss terms to be able to optimize. More generally, posing the solution of a PDE as an...

He is the director of the Center for Computational Geosciences and Optimization at the Institute for Computational Engineering and Sciences. Ghattas...

whose research concerns inverse problems, regularization, and PDE-constrained optimization, with applications including the mathematical modeling of piezoelectricity...

Solution of non-linear, eigenvalue and time-dependent problems. PDE-constrained optimization problems. Partitioning and load balancing of distributed data...

Demand optimization Destination dispatch — an optimization technique for dispatching elevators Energy minimization Entropy maximization Highly optimized tolerance...

Newton-type methods for large-scale optimization, simultaneous or one-shot methods for DAE and PDE constrained nonlinear optimization and optimal control problems...

and Optimization. Final Report SFB 359, Springer 2006 (The SFB # 359 was funded from 1993 to 2004.) as editor with others: Trends in PDE Constrained Optimization...

used in gas turbines in which gas expansion caused by heat release is constrained. First developed in the early 20th century as one of the earliest gas...

Anderson; Amsallem, David; Farhat, Charbel (2020). "Gradient-based constrained optimization using a database of linear reduced-order models". Journal of Computational...

algorithm of the method. Using a partial differential equation (PDE)-based method and solving the PDE equation by a numerical scheme, one can segment the image...

continuous and discrete integral transforms Constrained and unconstrained local and global optimization Statistics including model fitting, hypothesis...

boundary value problems (BVPs), that is, partial differential equations constrained by a set of boundary conditions, such as the Poisson's equation or the...

to reduce state saving overheads in parallel discrete event simulation (PDES). They define an approach based on reverse event codes (which can be automatically...

considered the solutions of the equation as rescalings of minima of a constrained optimization problem, based upon a modified Dirichlet energy. Making use of...

Levenberg-Marquardt Integration with HiOp. Built-in SLBQP optimizer Support for TAO- and nlopt-based constrained optimization solvers incorporating gradient and Hessian...

Analytical Design of Multi-loop PID Controllers, Optimization Based Controller Design for Constrained Optimal Control, Advanced Control for Thermally Coupled...

"D. Göddeke, 2010. Fast and Accurate Finite-Element Multigrid Solvers for PDE Simulations on GPU Clusters. Ph.D. dissertation, Technischen Universität...

Rabczuk, Timon (2021). "Isogeometric analysis for a phase-field constrained optimization problem of morphological evolution of vesicles in electrical fields"...

may be needed: for example, in fluid dynamics we conventionally close the PDEs for density, momentum and energy; yet in high speed flow especially at lower...

Emilio Gagliardo and Louis Nirenberg played a crucial role in the study of PDE solutions in L p {\displaystyle L^{p}} spaces. These inequalities provided...

1098/rspa.2017.0728. ISSN 1364-5021. Bertsekas, Dimitri P. (1996). Constrained optimization and Lagrange multiplier methods. Belmont, Mass.: Athena Scientific...