Projected Conjugate Gradient or BFGS for bound constrained optimization
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We know how projected gradient descent works for bound constrained optimization (https://neos-guide.org/content/gradient-projection-methods). It is basically steepest descent with an additional requirement of projecting the point back to the feasible region at each step. I have a nonlinear objective function subject to bound constraints on each variable.
Can we tailor conjugate gradient or BFGS using projections to solve the problem. So instead of steepest descent, each step will do CG or BFGS step, and if the new point goes beyond feasible region, we project it back to original region using projection like the one suggested in referred link. I know BFGS-B exists but I can't find any general theory for CG based approaches. Do we have a generalized theory or convergence results for all gradient/Hessian based approaches added with projection for bound constrained optimization.
optimization numerical-optimization gradient-descent
asked Jan 10 at 12:39
user402940user402940
1128
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add a comment |
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We know how projected gradient descent works for bound constrained optimization (https://neos-guide.org/content/gradient-projection-methods). It is basically steepest descent with an additional requirement of projecting the point back to the feasible region at each step. I have a nonlinear objective function subject to bound constraints on each variable.
Can we tailor conjugate gradient or BFGS using projections to solve the problem. So instead of steepest descent, each step will do CG or BFGS step, and if the new point goes beyond feasible region, we project it back to original region using projection like the one suggested in referred link. I know BFGS-B exists but I can't find any general theory for CG based approaches. Do we have a generalized theory or convergence results for all gradient/Hessian based approaches added with projection for bound constrained optimization.
optimization numerical-optimization gradient-descent
asked Jan 10 at 12:39
user402940user402940
1128
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The problem sounds "researchy" enough to be suitable for either mathoverflow or scicomp.stackexchange.com
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– zimbra314
Jan 10 at 13:41
add a comment |
$begingroup$
We know how projected gradient descent works for bound constrained optimization (https://neos-guide.org/content/gradient-projection-methods). It is basically steepest descent with an additional requirement of projecting the point back to the feasible region at each step. I have a nonlinear objective function subject to bound constraints on each variable.
Can we tailor conjugate gradient or BFGS using projections to solve the problem. So instead of steepest descent, each step will do CG or BFGS step, and if the new point goes beyond feasible region, we project it back to original region using projection like the one suggested in referred link. I know BFGS-B exists but I can't find any general theory for CG based approaches. Do we have a generalized theory or convergence results for all gradient/Hessian based approaches added with projection for bound constrained optimization.
optimization numerical-optimization gradient-descent
asked Jan 10 at 12:39
user402940user402940
1128
$endgroup$
We know how projected gradient descent works for bound constrained optimization (https://neos-guide.org/content/gradient-projection-methods). It is basically steepest descent with an additional requirement of projecting the point back to the feasible region at each step. I have a nonlinear objective function subject to bound constraints on each variable.
Can we tailor conjugate gradient or BFGS using projections to solve the problem. So instead of steepest descent, each step will do CG or BFGS step, and if the new point goes beyond feasible region, we project it back to original region using projection like the one suggested in referred link. I know BFGS-B exists but I can't find any general theory for CG based approaches. Do we have a generalized theory or convergence results for all gradient/Hessian based approaches added with projection for bound constrained optimization.
optimization numerical-optimization gradient-descent
optimization numerical-optimization gradient-descent
asked Jan 10 at 12:39
user402940user402940
1128
asked Jan 10 at 12:39
user402940user402940
1128
asked Jan 10 at 12:39
user402940user402940
1128
asked Jan 10 at 12:39
user402940user402940
1128
asked Jan 10 at 12:39
user402940user402940
1128
1128
$begingroup$
The problem sounds "researchy" enough to be suitable for either mathoverflow or scicomp.stackexchange.com
$endgroup$
– zimbra314
Jan 10 at 13:41
add a comment |
$begingroup$
The problem sounds "researchy" enough to be suitable for either mathoverflow or scicomp.stackexchange.com
$endgroup$
– zimbra314
Jan 10 at 13:41
$begingroup$
The problem sounds "researchy" enough to be suitable for either mathoverflow or scicomp.stackexchange.com
$endgroup$
– zimbra314
Jan 10 at 13:41
$begingroup$
The problem sounds "researchy" enough to be suitable for either mathoverflow or scicomp.stackexchange.com
$endgroup$
– zimbra314
Jan 10 at 13:41
add a comment |
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The problem sounds "researchy" enough to be suitable for either mathoverflow or scicomp.stackexchange.com
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– zimbra314
Jan 10 at 13:41